{"id":85316,"date":"2021-01-20T16:43:44","date_gmt":"2021-01-20T15:43:44","guid":{"rendered":"https:\/\/groupe-reussite.fr\/?page_id=85316"},"modified":"2024-02-29T19:24:19","modified_gmt":"2024-02-29T18:24:19","slug":"cours-en-ligne-arithmetique-seconde","status":"publish","type":"page","link":"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-arithmetique-seconde\/","title":{"rendered":"Cours en ligne arithm\u00e9tique seconde"},"content":{"rendered":"<div class=\"Latex_page\">\n<section class=\"has_ae_slider elementor-element elementor-section-full_width elementor-reverse-mobile elementor-section-stretched elementor-section-height-default elementor-section-height-default ae-bg-gallery-type-default elementor-section elementor-top-section\">\n<div class=\"elementor-container elementor-column-gap-no\">\n<div class=\"elementor-row\">\n<div class=\"elementor-column-wrap elementor-element-populated colone_elementor\">\n\t\t<div data-elementor-type=\"page\" data-elementor-id=\"88472\" class=\"elementor elementor-88472\">\n\t\t\t\t\t\t<div class=\"elementor-inner\">\n\t\t\t\t<div class=\"elementor-section-wrap\">\n\t\t\t\t\t\t\t\t\t<section class=\"has_ae_slider elementor-section elementor-top-section elementor-element elementor-element-e664302 elementor-section-content-bottom elementor-hidden-mobile wrap elementor-section-boxed elementor-section-height-default elementor-section-height-default ae-bg-gallery-type-default\" data-id=\"e664302\" data-element_type=\"section\" id=\"sticky_sidebar\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-no\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_ae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-d5b7bab strick_col ae-bg-gallery-type-default\" data-id=\"d5b7bab\" data-element_type=\"column\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-4b04bef elementor-headline--style-highlight elementor-widget elementor-widget-animated-headline\" data-id=\"4b04bef\" data-element_type=\"widget\" data-settings=\"{&quot;highlighted_text&quot;:&quot;r\\u00e9ussir en maths&quot;,&quot;headline_style&quot;:&quot;highlight&quot;,&quot;marker&quot;:&quot;circle&quot;,&quot;loop&quot;:&quot;yes&quot;,&quot;highlight_animation_duration&quot;:1200,&quot;highlight_iteration_delay&quot;:8000}\" data-widget_type=\"animated-headline.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<p class=\"elementor-headline\">\n\t\t\t\t\t<span class=\"elementor-headline-plain-text elementor-headline-text-wrapper\">Mon parcours pour<\/span>\n\t\t\t\t<span class=\"elementor-headline-dynamic-wrapper elementor-headline-text-wrapper\">\n\t\t\t\t\t<span class=\"elementor-headline-dynamic-text elementor-headline-text-active\">r\u00e9ussir en maths<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-533b999 elementor-position-left elementor-vertical-align-middle elementor-view-default elementor-mobile-position-top elementor-widget elementor-widget-icon-box\" data-id=\"533b999\" data-element_type=\"widget\" data-widget_type=\"icon-box.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-icon-box-wrapper\">\n\t\t\t\t\t\t<div class=\"elementor-icon-box-icon\">\n\t\t\t\t<span class=\"elementor-icon elementor-animation-\" >\n\t\t\t\t<i aria-hidden=\"true\" class=\"far fa-check-square\"><\/i>\t\t\t\t<\/span>\n\t\t\t<\/div>\n\t\t\t\t\t\t<div class=\"elementor-icon-box-content\">\n\t\t\t\t<p class=\"elementor-icon-box-title\">\n\t\t\t\t\t<span  >\n\t\t\t\t\t\tJ'aprends le cours par coeur\t\t\t\t\t<\/span>\n\t\t\t\t<\/p>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-9d143f0 elementor-position-left elementor-vertical-align-middle elementor-view-default elementor-mobile-position-top elementor-widget elementor-widget-icon-box\" data-id=\"9d143f0\" data-element_type=\"widget\" data-widget_type=\"icon-box.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-icon-box-wrapper\">\n\t\t\t\t\t\t<div class=\"elementor-icon-box-icon\">\n\t\t\t\t<span class=\"elementor-icon elementor-animation-\" >\n\t\t\t\t<i aria-hidden=\"true\" class=\"far fa-check-square\"><\/i>\t\t\t\t<\/span>\n\t\t\t<\/div>\n\t\t\t\t\t\t<div class=\"elementor-icon-box-content\">\n\t\t\t\t<p class=\"elementor-icon-box-title\">\n\t\t\t\t\t<span  >\n\t\t\t\t\t\tJe travaille avec un prof de maths\t\t\t\t\t<\/span>\n\t\t\t\t<\/p>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-a86028c elementor-position-left elementor-vertical-align-middle elementor-view-default elementor-mobile-position-top elementor-widget elementor-widget-icon-box\" data-id=\"a86028c\" data-element_type=\"widget\" data-widget_type=\"icon-box.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-icon-box-wrapper\">\n\t\t\t\t\t\t<div class=\"elementor-icon-box-icon\">\n\t\t\t\t<span class=\"elementor-icon elementor-animation-\" >\n\t\t\t\t<i aria-hidden=\"true\" class=\"far fa-check-square\"><\/i>\t\t\t\t<\/span>\n\t\t\t<\/div>\n\t\t\t\t\t\t<div class=\"elementor-icon-box-content\">\n\t\t\t\t<p class=\"elementor-icon-box-title\">\n\t\t\t\t\t<span  >\n\t\t\t\t\t\tJe travaille entre chaque s\u00e9ance\t\t\t\t\t<\/span>\n\t\t\t\t<\/p>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-4b5aa0f elementor-align-center elementor-widget elementor-widget-button\" data-id=\"4b5aa0f\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/cours-particuliers\/maths\/tous-niveaux\/france\/\" target=\"_blank\" class=\"elementor-button-link elementor-button elementor-size-lg\" role=\"button\" id=\"CTA_PAGE_CHAPEAU\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Cours particuliers maths<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-bdaf46b elementor-widget elementor-widget-text-editor\" data-id=\"bdaf46b\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\">\n\t\t\t\t<p style=\"text-align: center;\"><b>Avis Google France\u00a0<br \/><\/b><span style=\"font-size: 17px; color: #e5a430;\"><b>\u2605\u2605\u2605\u2605\u2605<\/b><\/span><b style=\"font-size: 17px;\"> 4,8 sur 5<\/b><\/p>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\n<\/div>\n<div class=\"elementor-column-wrap elementor-element-populated colone_latex\">\n<div class=\"style_pag\" style=\"color: #000;font-family: 'Lato', Sans-serif\">\n<div class=\"elementor-text-editor elementor-clearfix\">\n<h1 class=\"Latex_page_title\" style=\"text-align: center\">Cours d&rsquo;arithm\u00e9tique en seconde<\/h1>\n<\/div>\n<p class=\"colone_latex_ancres\" style=\"text-align: center\"><a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-arithmetique-seconde\/\">R\u00e9sum\u00e9 de cours<\/a> <a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-exercices-corriges-arithmetique-seconde\/\">Exercices et corrig\u00e9s<\/a><\/p>\n<p class=\"colone_latex_ancres\" style=\"text-align: center\"><a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-maths-seconde\/\">Cours en ligne de Maths en Seconde<\/a><\/p>\n<div>Ce chapitre d&rsquo;Arithm\u00e9tique est g\u00e9n\u00e9ralement trait\u00e9 en d\u00e9but d&rsquo;ann\u00e9e de seconde avec le chapitre sur les ensembles. Ensuite sont trait\u00e9s diff\u00e9rentes chapitres sur les fonctions : g\u00e9n\u00e9ralit\u00e9s sur les fonctions, variations de fonctions et fonctions affines notamment.<\/div>\n<div>\n<div id=\"message-text-8e016fa4-495e-4e71-9228-2b036b75201c\" class=\"markdown prose w-full flex flex-col break-words dark:prose-invert dark\">\n<p>&nbsp;<\/p>\n<p>N\u2019h\u00e9site pas \u00e0 prendre un <a href=\"https:\/\/groupe-reussite.fr\/cours-particuliers\/maths\/tous-niveaux\/france\/\">prof de maths<\/a> qui offre l&rsquo;avantage de pouvoir suivre un programme de seconde personnalis\u00e9 en fonction de tes besoins sp\u00e9cifiques, ce qui peut grandement contribuer \u00e0 sa r\u00e9ussite en Arithm\u00e9tique.<\/p>\n<\/div>\n<\/div>\n<h2>1. Arithm\u00e9tique en 2nde : Multiples et diviseurs<\/h2>\n<p><span style=\"text-decoration: underline\"><strong>a) D\u00e9finitions<\/strong><\/span><\/p>\n<p>Soit n un nombre entier (naturel ou relatif ).<\/p>\n<p><img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-2b6e225d778ccd32cb2bd9cc4eaead9a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#117;&#108;&#108;&#101;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"7\" width=\"8\" style=\"vertical-align: 1px;\"\/> On appelle diviseurs de <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-b170995d512c659d8668b4e42e1fef6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"\/> tous les nombres entiers <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-ac7da57d7f507262338bb5168feb3e06_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#113;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: -4px;\"\/> tels que<\/p>\n<p><img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-99f4f8ac35e2dcd223ecd8e4cc31a576_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#110;&#125;&#123;&#113;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"11\" style=\"vertical-align: -16px;\"\/> <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-478c7dbb76fc8e5b0b52edad79847b31_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#105;&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"10\" style=\"vertical-align: -1px;\"\/> <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-e1ac530f2a83951115df3e0daa67b801_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#109;&#97;&#116;&#104;&#98;&#98;&#123;&#90;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"12\" style=\"vertical-align: 0px;\"\/> (ensemble des entiers relatifs).<\/p>\n<p><img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-2b6e225d778ccd32cb2bd9cc4eaead9a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#117;&#108;&#108;&#101;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"7\" width=\"8\" style=\"vertical-align: 1px;\"\/> On appelle multiples de <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-b170995d512c659d8668b4e42e1fef6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"\/> tous les nombres de la forme <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-ce9e7771391f8593247450c4153013a3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#107;&#32;&#92;&#116;&#105;&#109;&#101;&#115;&#32;&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"42\" style=\"vertical-align: 0px;\"\/>, o\u00f9 <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-3422b6bb5c160593658b7c39425d9880_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#107;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"9\" style=\"vertical-align: 0px;\"\/> <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-478c7dbb76fc8e5b0b52edad79847b31_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#105;&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"10\" style=\"vertical-align: -1px;\"\/> <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-e1ac530f2a83951115df3e0daa67b801_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#109;&#97;&#116;&#104;&#98;&#98;&#123;&#90;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"12\" style=\"vertical-align: 0px;\"\/>.<\/p>\n<ul>\n<li style=\"list-style-type: none\">\n<ul>\n<li>Remarque : Si <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-ac7da57d7f507262338bb5168feb3e06_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#113;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: -4px;\"\/> est un diviseur de <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-b170995d512c659d8668b4e42e1fef6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"\/> alors on dit que <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-b170995d512c659d8668b4e42e1fef6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"\/> est divisible par <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-ac7da57d7f507262338bb5168feb3e06_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#113;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: -4px;\"\/>.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>Exemple : 2 est-il un diviseur de 12 ?<\/p>\n<p>2 est un diviseur de 12 car <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-fe582afd62cc5b8663a35d402f09e90c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#49;&#50;&#125;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"18\" style=\"vertical-align: -12px;\"\/> = 6 <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-478c7dbb76fc8e5b0b52edad79847b31_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#105;&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"10\" style=\"vertical-align: -1px;\"\/> <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-e1ac530f2a83951115df3e0daa67b801_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#109;&#97;&#116;&#104;&#98;&#98;&#123;&#90;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"12\" style=\"vertical-align: 0px;\"\/>.<\/p>\n<p><span style=\"text-decoration: underline\"><strong>b) Crit\u00e8res de divisibilit\u00e9<\/strong><\/span><\/p>\n<p>Un crit\u00e8re de divisibilit\u00e9 est une r\u00e8gle permettant de savoir si un entier est divisible par un autre entier.<\/p>\n<p><strong>1- Crit\u00e8re de divisibilit\u00e9 par 2<\/strong><\/p>\n<ul>\n<li>Propri\u00e9t\u00e9 : Un entier est divisible par 2 si son chiffre des unit\u00e9s est 0, 2, 4, 6 ou 8\n<ul>\n<li>Remarque : Quand un entier est divisible par 2, on dit qu\u2019il est pair. Sinon, on dit qu\u2019il est impair.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>Exemple : 77 est -il divisible par 2 ?<\/p>\n<p>77 n&rsquo;est pas divisible par 2 car son chiffre des unit\u00e9s est 7.<\/p>\n<ul>\n<li>Propri\u00e9t\u00e9<\/li>\n<\/ul>\n<p>Si <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-b170995d512c659d8668b4e42e1fef6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"\/> est pair alors il existe un entier <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-3422b6bb5c160593658b7c39425d9880_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#107;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"9\" style=\"vertical-align: 0px;\"\/> tel que <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-6e6a566793afcb732482cd68f2d360d7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#32;&#61;&#32;&#50;&#107;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"52\" style=\"vertical-align: 0px;\"\/>.<\/p>\n<p>Si <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-b170995d512c659d8668b4e42e1fef6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"\/> est impair alors il existe un entier <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-3422b6bb5c160593658b7c39425d9880_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#107;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"9\" style=\"vertical-align: 0px;\"\/> tel que <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-25049a95a63208ee634855ecaad49ec3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#32;&#61;&#32;&#50;&#107;&#32;&#43;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"83\" style=\"vertical-align: -2px;\"\/>.<\/p>\n<p><strong>2- Crit\u00e8re de divisibilit\u00e9 par 3<\/strong><\/p>\n<ul>\n<li>Propri\u00e9t\u00e9 : Un entier est divisible par 3 si la somme de ses chiffres est elle-m\u00eame divisible par 3.<\/li>\n<\/ul>\n<p>Exemple : 123 est-il divisible par 3 ?<\/p>\n<p>123 est divisible par 3 car la somme de ses chiffres est 1+2+3 = 6, et 6 est divisible par 3.<\/p>\n<p><strong>3- Crit\u00e8re de divisibilit\u00e9 par 5<\/strong><\/p>\n<ul>\n<li>Propri\u00e9t\u00e9 : Un entier est divisible par 5 si son chiffre des unit\u00e9s est 0 ou 5.<\/li>\n<\/ul>\n<p><strong>4- Une propri\u00e9t\u00e9 importante<\/strong><\/p>\n<ul>\n<li>Propri\u00e9t\u00e9 : Soient <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-3bf85f1087e9fbed3a319341134ac1a2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#112;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"10\" style=\"vertical-align: -4px;\"\/> et <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-ac7da57d7f507262338bb5168feb3e06_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#113;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: -4px;\"\/> deux entiers. Un entier <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-b170995d512c659d8668b4e42e1fef6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"\/> est divisible par <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-b2e79cd96043c68fc4da2c14078f84d9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#112;&#32;&#92;&#116;&#105;&#109;&#101;&#115;&#32;&#113;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"40\" style=\"vertical-align: -4px;\"\/> si et seulement si il est divisible par <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-3bf85f1087e9fbed3a319341134ac1a2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#112;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"10\" style=\"vertical-align: -4px;\"\/> et <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-ac7da57d7f507262338bb5168feb3e06_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#113;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: -4px;\"\/>.<\/li>\n<\/ul>\n<p><span style=\"text-decoration: underline\"><strong>c) Somme de deux multiples<\/strong><\/span><\/p>\n<ul>\n<li>Propri\u00e9t\u00e9 : Soient <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"\/> un entier relatif. Soient <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-6b41df788161942c6f98604d37de8098_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"15\" style=\"vertical-align: 0px;\"\/> et <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-b170995d512c659d8668b4e42e1fef6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"\/> deux entiers multiples de <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"\/>.<\/li>\n<\/ul>\n<p>Alors <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-6b41df788161942c6f98604d37de8098_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"15\" style=\"vertical-align: 0px;\"\/> + <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-b170995d512c659d8668b4e42e1fef6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"\/> est un multiple de <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"\/><\/p>\n<ul>\n<li style=\"list-style-type: none\">\n<ul>\n<li>D\u00e9monstration : m est un multiple de a donc il existe un entier k tel que <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-9a464280fd89ead9770cbdfbc9177945_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#32;&#61;&#32;&#107;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"58\" style=\"vertical-align: 0px;\"\/>.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>De m\u00eame, n est un multiple de a donc il existe un entier <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-20978fc71e693c6b0ca59b41daaed2b9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#107;&#39;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"14\" style=\"vertical-align: 0px;\"\/> tel que <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-ae4ec01ffeff5bdb0e71a6829f9f3d35_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#32;&#61;&#32;&#107;&#39;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"58\" style=\"vertical-align: 0px;\"\/>.<\/p>\n<p>Ainsi, <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-c7fd35c6946454a03e2d8240a826c4cf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#32;&#43;&#110;&#32;&#61;&#32;&#107;&#97;&#32;&#43;&#107;&#39;&#97;&#32;&#61;&#32;&#40;&#107;&#32;&#43;&#107;&#39;&#41;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"228\" style=\"vertical-align: -5px;\"\/>.<\/p>\n<p>Or, <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-3422b6bb5c160593658b7c39425d9880_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#107;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"9\" style=\"vertical-align: 0px;\"\/> <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-478c7dbb76fc8e5b0b52edad79847b31_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#105;&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"10\" style=\"vertical-align: -1px;\"\/> <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-e1ac530f2a83951115df3e0daa67b801_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#109;&#97;&#116;&#104;&#98;&#98;&#123;&#90;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"12\" style=\"vertical-align: 0px;\"\/> et <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-20978fc71e693c6b0ca59b41daaed2b9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#107;&#39;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"14\" style=\"vertical-align: 0px;\"\/> <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-478c7dbb76fc8e5b0b52edad79847b31_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#105;&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"10\" style=\"vertical-align: -1px;\"\/> <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-e1ac530f2a83951115df3e0daa67b801_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#109;&#97;&#116;&#104;&#98;&#98;&#123;&#90;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"12\" style=\"vertical-align: 0px;\"\/> donc <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-bdeac65a890a9e44b02af089dc522762_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#107;&#32;&#43;&#107;&#39;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"45\" style=\"vertical-align: -2px;\"\/> <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-478c7dbb76fc8e5b0b52edad79847b31_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#105;&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"10\" style=\"vertical-align: -1px;\"\/> <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-e1ac530f2a83951115df3e0daa67b801_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#109;&#97;&#116;&#104;&#98;&#98;&#123;&#90;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"12\" style=\"vertical-align: 0px;\"\/>. Ainsi, <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-062ab19758ee113bd0497abcc14e27db_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#40;&#107;&#32;&#43;&#107;&#39;&#41;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"68\" style=\"vertical-align: -5px;\"\/> est un multiple de <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"\/>.<\/p>\n<p>Donc <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-338da7b315315e3fe566ee209f2da9ac_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#32;&#43;&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"48\" style=\"vertical-align: -2px;\"\/> est un multiple de <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"\/>.<\/p>\n<p><span style=\"text-decoration: underline\"><strong>d) Carr\u00e9 d&rsquo;un nombre impair<\/strong><\/span><\/p>\n<ul>\n<li>Propri\u00e9t\u00e9 : Soit <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"\/> un nombre impair.<\/li>\n<\/ul>\n<p>Alors, <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-22833c67f596bd1558c13d959f069ecb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&sup2;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"\/>est impair.<\/p>\n<ul>\n<li style=\"list-style-type: none\">\n<ul>\n<li>D\u00e9monstration :<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>Si <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"\/> est impair alors il existe un entier <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-3422b6bb5c160593658b7c39425d9880_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#107;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"9\" style=\"vertical-align: 0px;\"\/> tel que : <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-b9a999bf6fd5765d7d83c3ee10efccf8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#32;&#61;&#32;&#50;&#107;&#32;&#43;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"81\" style=\"vertical-align: -2px;\"\/>.<\/p>\n<p>Ainsi, <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-bd0cf046ce1831368e01d295108485ea_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&sup2;&#32;&#61;&#32;&#40;&#50;&#107;&#32;&#43;&#49;&#41;&sup2;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"95\" style=\"vertical-align: -5px;\"\/><\/p>\n<p>= (2<img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-3422b6bb5c160593658b7c39425d9880_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#107;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"9\" style=\"vertical-align: 0px;\"\/>)\u00b2 +2 \u00d7 2<img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-3422b6bb5c160593658b7c39425d9880_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#107;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"9\" style=\"vertical-align: 0px;\"\/> \u00d7 1 + 1\u00b2 = <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-6ef321cf27693326a472cefe16529e85_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#107;&sup2;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\"\/> + 4<img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-3422b6bb5c160593658b7c39425d9880_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#107;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"9\" style=\"vertical-align: 0px;\"\/> + 1.<\/p>\n<p>Or, <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-1f6c014103e7ca6812e2638f394fd4ec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#107;&sup2;&#32;&#61;&#32;&#50;&times;&#50;&#107;&sup2;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"69\" style=\"vertical-align: 0px;\"\/> et <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-ea66e2bec2d04c17ea7f8708cecc858a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#107;&#32;&#61;&#32;&#50;&times;&#50;&#107;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"69\" style=\"vertical-align: 0px;\"\/> donc ce sont deux nombres pairs.<\/p>\n<p>Ainsi, leur somme est aussi paire. Donc, quand on ajoute 1 \u00e0 cette somme, cela donne un r\u00e9sultat impair.<\/p>\n<p>Par cons\u00e9quent, <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-ca5c6388688d27d1d79cb0d2abd05440_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#107;&sup2;&#32;&#43;&#52;&#107;&#32;&#43;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"89\" style=\"vertical-align: -2px;\"\/> est impair, donc <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-22833c67f596bd1558c13d959f069ecb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&sup2;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"\/> est impair.<\/p>\n<p>&nbsp;<\/p>\n\t\t<div data-elementor-type=\"section\" data-elementor-id=\"184597\" class=\"elementor elementor-184597\">\n\t\t\t\t\t<div class=\"elementor-section-wrap\">\n\t\t\t\t\t\t\t\t<section class=\"has_ae_slider elementor-section elementor-inner-section elementor-element elementor-element-f6a24df elementor-section-content-bottom full_width elementor-section-full_width elementor-section-height-min-height elementor-section-height-default ae-bg-gallery-type-default\" data-id=\"f6a24df\" data-element_type=\"section\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-narrow\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_ae_slider elementor-column elementor-col-66 elementor-inner-column elementor-element elementor-element-1a43b36a ae-bg-gallery-type-default\" data-id=\"1a43b36a\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-51eac563 elementor-widget elementor-widget-heading\" data-id=\"51eac563\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">PROF DE MATHS PARTICULIER<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-51d48fa4 elementor-widget elementor-widget-heading\" data-id=\"51d48fa4\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">Des cours de qualit\u00e9 et enseignants aguerris<\/h4>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-7fd3aeff elementor-widget elementor-widget-heading\" data-id=\"7fd3aeff\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">Pr\u00e9parer des concours ou s'exercer<\/h4>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-691aa52c elementor-align-left elementor-mobile-align-center elementor-widget elementor-widget-button\" data-id=\"691aa52c\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/cours-particuliers\/maths\/tous-niveaux\/france\/\" target=\"_blank\" class=\"elementor-button-link elementor-button elementor-size-md\" role=\"button\" id=\"CTA_PRD_CP\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Cours de maths \u00e0 domicile<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-266b70e2 elementor-widget elementor-widget-text-editor\" data-id=\"266b70e2\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\">\n\t\t\t\t<p style=\"text-align: left\"><b>Avis Google France <\/b><span style=\"color: #e5a430\"><b>\u2605\u2605\u2605\u2605\u2605<\/b><\/span><b> 4,9 sur 5<\/b><\/p>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"has_ae_slider elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-4bbd68df ae-bg-gallery-type-default\" data-id=\"4bbd68df\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\n<p>&nbsp;<\/p>\n<h2>2. Arithm\u00e9tique seconde PPCM et PGCD<\/h2>\n<p><span style=\"text-decoration: underline\"><strong>a) PPCM<\/strong><\/span><\/p>\n<ul>\n<li>D\u00e9finition : Soient <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"\/> et <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\"\/> deux entiers.<\/li>\n<\/ul>\n<p>On appelle ppcm (plus petit commun multiple) de <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"\/> et <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\"\/> le plus petit nombre <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-6b41df788161942c6f98604d37de8098_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"15\" style=\"vertical-align: 0px;\"\/> qui est \u00e0 la fois multiple de <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"\/> et de <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\"\/>.<\/p>\n<p>On le note ppcm(<img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"\/> ; <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\"\/>).<\/p>\n<p>Exemple : Que vaut ppcm(6,15) ?<\/p>\n<p>Si <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"\/> = 6 et <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\"\/> = 15, alors<\/p>\n<p>ppcm(6; 15) = 30 car :<\/p>\n<p><img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-2b6e225d778ccd32cb2bd9cc4eaead9a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#117;&#108;&#108;&#101;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"7\" width=\"8\" style=\"vertical-align: 1px;\"\/> les multiples de 6 sont : 6, 12, 18, 24, 30, 36, etc.<\/p>\n<p><img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-2b6e225d778ccd32cb2bd9cc4eaead9a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#117;&#108;&#108;&#101;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"7\" width=\"8\" style=\"vertical-align: 1px;\"\/> les multiples de 15 sont : 15, 30, 45, etc.<\/p>\n<p>Le plus petit multiple commun est donc 30.<\/p>\n<p><span style=\"text-decoration: underline\"><strong>b) PGCD<\/strong><\/span><\/p>\n<ul>\n<li>D\u00e9finition : Soient <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"\/> et <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\"\/> deux entiers.<\/li>\n<\/ul>\n<p>On appelle pgcd (plus grand commun diviseur) de <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"\/> et <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\"\/> le plus grand nombre <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-4e8716946f6a868f015e0d62f28bc540_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#100;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"10\" style=\"vertical-align: 0px;\"\/> qui divise \u00e0 la fois <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"\/> et <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\"\/>.<\/p>\n<p>On le note pgcd(<img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"\/> ; <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\"\/>).<\/p>\n<p>Exemple : Que vaut pgcd(210 ; 49) ?<\/p>\n<p>Si <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"\/> = 210 et <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\"\/> = 49 alors pgcd(201; 49) = 7 car :<\/p>\n<p><img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-2b6e225d778ccd32cb2bd9cc4eaead9a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#117;&#108;&#108;&#101;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"7\" width=\"8\" style=\"vertical-align: 1px;\"\/> 210 = 2\u00d73\u00d75\u00d77. Les diviseurs de 210 sont donc :<\/p>\n<p>{1 ; 2 ; 3 ; 5 ; 7 ; 2 x 3 = 6 ;<\/p>\n<p>2 x 5 = 10 ; 2 x 7 = 14 ; 5 x 3 = 15<\/p>\n<p>7 x 3 = 21 ; 2 x 3 x 5 = 30 ;<\/p>\n<p>5 x 7 = 35 ; 2 x 3 x 7 = 42 ;<\/p>\n<p>3 x 5 x 7 = 105 ;<\/p>\n<p>2 x 3 x 5 x 7 = 210}<\/p>\n<p><img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-2b6e225d778ccd32cb2bd9cc4eaead9a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#117;&#108;&#108;&#101;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"7\" width=\"8\" style=\"vertical-align: 1px;\"\/> 49 = 7\u00d77<\/p>\n<p>Ainsi, le plus grand diviseur commun est 7.<\/p>\n<ul>\n<li>Propri\u00e9t\u00e9<\/li>\n<\/ul>\n<p>Soient <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"\/> et <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\"\/> deux entiers naturels tels que <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-13fad2f9dec1b49ba5858a35b588c528_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#32;&#61;&#32;&#98;&#113;&#32;&#43;&#114;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"79\" style=\"vertical-align: -4px;\"\/> ,<\/p>\n<p>0 <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-64bf79929b9db15a97919ced3ea3a383_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#113;&#115;&#108;&#97;&#110;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"12\" style=\"vertical-align: -3px;\"\/> <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-0035068ab84b168584214c75fee7ef3f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#114;&#32;&#60;&#32;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"40\" style=\"vertical-align: -2px;\"\/> et <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-ac7da57d7f507262338bb5168feb3e06_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#113;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: -4px;\"\/> \u2208 <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-bc8e16cdad5408a0b540d2bc0098bcfb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#109;&#97;&#116;&#104;&#98;&#98;&#123;&#78;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"13\" style=\"vertical-align: 0px;\"\/>.<\/p>\n<p>Alors, pgcd(<img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"\/> ; <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\"\/>) = pgcd(<img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\"\/> ; <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-c409433a9e2dfcdb83360a974d243f18_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#114;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"\/> ).<\/p>\n<p>Pour calculer le pgcd de deux nombres, on utilisera la propri\u00e9t\u00e9 pr\u00e9c\u00e9dente autant que n\u00e9cessaire. Par exemple, pour calculer pgcd(126; 24) :<\/p>\n<p><img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-2b6e225d778ccd32cb2bd9cc4eaead9a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#117;&#108;&#108;&#101;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"7\" width=\"8\" style=\"vertical-align: 1px;\"\/> on \u00e9crit d\u2019abord que 126 = 5\u00d724+6, donc pgcd(126; 24) = pgcd(24; 6);<\/p>\n<p><img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-2b6e225d778ccd32cb2bd9cc4eaead9a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#117;&#108;&#108;&#101;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"7\" width=\"8\" style=\"vertical-align: 1px;\"\/> on \u00e9crit ensuite que 24 = 4\u00d76+0, donc pgcd(24; 6) = pgcd(6; 0) = 6.<\/p>\n<p>L\u2019\u00e9criture <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-13fad2f9dec1b49ba5858a35b588c528_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#32;&#61;&#32;&#98;&#113;&#32;&#43;&#114;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"79\" style=\"vertical-align: -4px;\"\/> est appel\u00e9e la division euclidienne de <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"\/> par <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\"\/>.<\/p>\n<p>Le fait d\u2019\u00e9crire les divisions euclidiennes successives tel que nous l\u2019avons fait constitue ce que l\u2019on nomme l\u2019algorithme d\u2019Euclide.<\/p>\n<ul>\n<li>Propri\u00e9t\u00e9<\/li>\n<\/ul>\n<p>Soient <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"\/> et <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\"\/> deux entiers naturels. Alors, pgcd(<img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"\/> ; <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\"\/>) est le dernier reste non nul dans l\u2019algorithme d\u2019Euclide.<\/p>\n<p>Exemple<\/p>\n<p><img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"\/> = 775 et <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\"\/> = 372.<\/p>\n<p>L\u2019algorithme d\u2019Euclide donne :<\/p>\n<p>775 = 2\u00d7372+ 31<\/p>\n<p>372 = 12\u00d731+0.<\/p>\n<p>Le dernier reste non nul est 31 donc pgcd(775; 372) = 31.<\/p>\n<ul>\n<li>Propri\u00e9t\u00e9<\/li>\n<\/ul>\n<p>pgcd(<img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"\/> ; <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\"\/>) = 1 <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-5cd43923bb87ebb8043e0d2d285190fb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#105;&#102;&#102;\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"32\" style=\"vertical-align: -1px;\"\/> <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-99534c1ecfde742c18bea75de44594b4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#97;&#125;&#123;&#98;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"10\" style=\"vertical-align: -12px;\"\/> est irr\u00e9ductible.<\/p>\n<p>Si <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-99534c1ecfde742c18bea75de44594b4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#97;&#125;&#123;&#98;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"10\" style=\"vertical-align: -12px;\"\/> n\u2019est pas irr\u00e9ductible alors on divise a et b par pgcd(a ; b) pour simplifier au maximum la fraction.<\/p>\n<p>Exemple<\/p>\n<p>pgcd(775; 372) = 31 (voir exemple pr\u00e9c\u00e9dent) donc<\/p>\n<p><img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-439e5aefd2517867b928078992896305_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#55;&#55;&#53;&#125;&#123;&#51;&#55;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"27\" style=\"vertical-align: -12px;\"\/> = <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-79eae232b920c327d715a91c740e3b9b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#55;&#55;&#53;&divide;&#51;&#49;&#125;&#123;&#51;&#55;&#50;&divide;&#51;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"45\" style=\"vertical-align: -12px;\"\/> =<img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-73d987461ae22c3cc057e70a5b4a7b16_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#50;&#53;&#125;&#123;&#49;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"18\" style=\"vertical-align: -12px;\"\/>.<\/p>\n<ul>\n<li>Propri\u00e9t\u00e9<\/li>\n<\/ul>\n<p>Pour tous entiers naturels <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"\/> et <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\"\/>, ppcm(<img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"\/> ; <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\"\/>) <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-3e2a3b7b9d8913e71519bf7df9eb51b3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#105;&#109;&#101;&#115;\" title=\"Rendered by QuickLaTeX.com\" height=\"9\" width=\"10\" style=\"vertical-align: 0px;\"\/> pgcd(<img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"\/> ; <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\"\/>) = <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-7202c73e2795274765d7f01eefc3e3f5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"17\" style=\"vertical-align: 0px;\"\/>.<\/p>\n<p>&nbsp;<\/p>\n\t\t<div data-elementor-type=\"section\" data-elementor-id=\"186409\" class=\"elementor elementor-186409\">\n\t\t\t\t\t<div class=\"elementor-section-wrap\">\n\t\t\t\t\t\t\t\t<section class=\"has_ae_slider elementor-section elementor-inner-section elementor-element elementor-element-208557d4 elementor-section-content-bottom full_width elementor-section-full_width elementor-section-height-min-height elementor-section-height-default ae-bg-gallery-type-default\" data-id=\"208557d4\" data-element_type=\"section\" data-settings=\"{&quot;background_background&quot;:&quot;gradient&quot;}\">\n\t\t\t\t\t\t\t<div class=\"elementor-background-overlay\"><\/div>\n\t\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-narrow\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_ae_slider elementor-column elementor-col-50 elementor-inner-column elementor-element elementor-element-5c1307a9 ae-bg-gallery-type-default\" data-id=\"5c1307a9\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-a42a1b elementor-widget elementor-widget-heading\" data-id=\"a42a1b\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">AVOIR LES MEILLEURS PROFS DE MATHS<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-53b6892b elementor-widget elementor-widget-heading\" data-id=\"53b6892b\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">C'est gagner en autonomie<\/h4>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-339aefc1 elementor-align-left elementor-mobile-align-center elementor-widget elementor-widget-button\" data-id=\"339aefc1\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/cours-particuliers\/maths\/tous-niveaux\/france\/\" target=\"_blank\" class=\"elementor-button-link elementor-button elementor-size-md\" role=\"button\" id=\"CTA_PRD_CP\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Cours de maths particulier<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"has_ae_slider elementor-column elementor-col-50 elementor-inner-column elementor-element elementor-element-461d5d63 ae-bg-gallery-type-default\" data-id=\"461d5d63\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\n<p>&nbsp;<\/p>\n<h2>3. Arithm\u00e9tique en seconde: Nombres premiers<\/h2>\n<p><span style=\"text-decoration: underline\"><strong>a) D\u00e9finition<\/strong><\/span><\/p>\n<ul>\n<li>D\u00e9finition : Un entier naturel est premier s\u2019il admet deux uniques diviseurs : 1 et lui-m\u00eame.\n<ul>\n<li>Remarque : Le nombre \u00ab 1 \u00bb n\u2019est pas premier car il n\u2019admet qu\u2019un seul diviseur (et non 2). La liste des nombres premiers commence ainsi : 2 ; 3 ; 5 ; 7 ; 11 ; 13 ;17 ; 19 ; 23&#8230;<\/li>\n<li>Remarque : Cette liste ne s\u2019arr\u00eate pas; on dit que l\u2019ensemble des nombres premiers est infini (mais ce n\u2019est pas au programme&#8230;).<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p><span style=\"text-decoration: underline\"><strong>b) D\u00e9composition en produit de facteurs premiers<\/strong><\/span><\/p>\n<ul>\n<li>Propri\u00e9t\u00e9 : Tout entier naturel <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"\/> s\u2019\u00e9crit de mani\u00e8re unique sous la forme :<\/li>\n<\/ul>\n<p><img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-bc257f5ce8889d758d5c3903c9dd7a74_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#32;&#61;&#32;&#112;&#95;&#49;&#94;&#123;&alpha;&#95;&#49;&#125;&#32;&#92;&#116;&#105;&#109;&#101;&#115;&#32;&#112;&#95;&#50;&#94;&#123;&alpha;&#95;&#50;&#125;&#32;&#92;&#116;&#105;&#109;&#101;&#115;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"100\" style=\"vertical-align: -5px;\"\/> &#8230; <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-ad71b3625d7f8ef09a7c37f7affca026_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#105;&#109;&#101;&#115;&#32;&#112;&#95;&#110;&#94;&#123;&alpha;&#95;&#110;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"29\" style=\"vertical-align: -4px;\"\/><\/p>\n<p>o\u00f9 <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-c7bab69bae9bcd6c8e2b54aceb92ec73_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#112;&#95;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"16\" style=\"vertical-align: -4px;\"\/>, <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-b1f827f8a6c983b3db402a6b39a19a6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#112;&#95;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"17\" style=\"vertical-align: -4px;\"\/>, &#8230;, <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-c5f85d4688e53d2c213031fea83a6206_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#112;&#95;&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: -4px;\"\/> sont des nombres premiers et o\u00f9 <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-5564b12dccdbbd14c915c4c377bfe908_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&alpha;&#95;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"9\" width=\"5\" style=\"vertical-align: -3px;\"\/>, <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-e2be0513162dc2c11c640a47c63a3418_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&alpha;&#95;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"9\" width=\"7\" style=\"vertical-align: -3px;\"\/>, &#8230;, <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-e6910d368dbf637e9424013d7f0d0728_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&alpha;&#95;&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"6\" width=\"8\" style=\"vertical-align: -3px;\"\/> sont des entiers naturels.<\/p>\n<p>Exemple :\u00a0360 = <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-0549f5f896f19f3f61957391fc097e3e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#94;&#123;&#51;&#125;&#32;&#92;&#116;&#105;&#109;&#101;&#115;&#32;&#51;&#94;&#123;&#50;&#125;&#32;&#92;&#116;&#105;&#109;&#101;&#115;&#32;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"84\" style=\"vertical-align: 0px;\"\/>.<\/p>\n<p>Pour trouver cette d\u00e9composition, on peut diviser autant que n\u00e9cessaire par 2, puis par 3, puis par 5, etc.<\/p>\n<p><img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-d4c09053fe14e957e42d06df916e55bd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#51;&#54;&#48;&#125;&#32;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"27\" style=\"vertical-align: -12px;\"\/> = 180 (on divise par 2 car 360 est pair)<\/p>\n<p><img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-4476907b49b4acdc85d99544e1371969_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#49;&#56;&#48;&#125;&#32;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"27\" style=\"vertical-align: -12px;\"\/> = 90 (on divise par 2 car 180 est pair)<\/p>\n<p><img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-8550fac18b6df4d75525a83cdf0da5c9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#57;&#48;&#125;&#32;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"18\" style=\"vertical-align: -12px;\"\/> = 45 (on divise par 2 car 90 est pair)<\/p>\n<p><img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-74cd56532f578007737b45f2daeb78fb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#52;&#53;&#125;&#32;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"18\" style=\"vertical-align: -12px;\"\/> = 15 (on divise par 3 car 45 n&rsquo;est plus divisible par 2, donc on passe au nombre premier suivant)<\/p>\n<p><img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-a4a9556931f4c1bcf742341467d2a3fe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#49;&#53;&#125;&#32;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"18\" style=\"vertical-align: -12px;\"\/> = 5 (on continue \u00e0 diviser par 3)<\/p>\n<p><img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-b131ca4edb3f7f4161a2d68d1c58f7cf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#53;&#125;&#32;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"9\" style=\"vertical-align: -12px;\"\/> = 1 (on passe \u00e0 5 qui vient apr\u00e8s 3)<\/p>\n<p>On s&rsquo;arr\u00eate quand on obtient 1.<\/p>\n<p>On a ainsi obtenu que 360 = 2 \u00d7 2 \u00d7 2 \u00d7 3 \u00d7 3 \u00d7 5.<\/p>\n<p>Retrouvez d&rsquo;autres cours en ligne de maths seconde sur notre site :<\/p>\n<ul>\n<li><a class=\"waffle-rich-text-link\" href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-generalites-fonctions-seconde\/\">Cours complet sur les g\u00e9n\u00e9ralit\u00e9s sur les fonctions en seconde<\/a><\/li>\n<li><a class=\"waffle-rich-text-link\" href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-variation-fonction-seconde\/\">Fiche de cours sur les fonctions et variations en seconde g\u00e9n\u00e9rale<\/a><\/li>\n<li><a class=\"waffle-rich-text-link\" href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-fonction-affine-seconde\/\">Cours de fonctions affines 2nde<\/a><\/li>\n<li><a class=\"waffle-rich-text-link\" href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-maths-fonctions-reference-seconde\/\">R\u00e9sum\u00e9 de cours sur les fonctions de r\u00e9f\u00e9rence en classe de seconde<\/a><\/li>\n<li><a class=\"waffle-rich-text-link\" href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-exercices-corriges-arithmetique-seconde\/\">Exercices et corrig\u00e9s sur l&rsquo;arithm\u00e9tique en seconde<\/a><\/li>\n<li><a class=\"waffle-rich-text-link\" href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-exercices-corriges-generalites-fonctions-seconde\/\">\u00c9valuations et corrig\u00e9s g\u00e9n\u00e9ralit\u00e9s sur les fonctions seconde<\/a><\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Cours d&rsquo;arithm\u00e9tique en seconde R\u00e9sum\u00e9 de cours Exercices et corrig\u00e9s Cours en ligne de Maths en Seconde Ce chapitre d&rsquo;Arithm\u00e9tique est g\u00e9n\u00e9ralement trait\u00e9 en d\u00e9but d&rsquo;ann\u00e9e de seconde avec le chapitre sur les ensembles. Ensuite sont trait\u00e9s diff\u00e9rentes chapitres sur les fonctions : g\u00e9n\u00e9ralit\u00e9s sur les fonctions, variations de fonctions et fonctions affines notamment. &nbsp; [&hellip;]<\/p>\n","protected":false},"author":6,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.2.1 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>R\u00e9sum\u00e9 de cours et m\u00e9thodes : l&#039;arithm\u00e9tique en seconde g\u00e9n\u00e9rale<\/title>\n<meta name=\"description\" content=\"cours de maths sur l&#039;arithm\u00e9tique en seconde g\u00e9n\u00e9rale : multiple et diviseur, PPCM et PGCD, nombres premiers etc..\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-arithmetique-seconde\/\" \/>\n<meta property=\"og:locale\" content=\"fr_FR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"R\u00e9sum\u00e9 de cours et m\u00e9thodes : l&#039;arithm\u00e9tique en seconde g\u00e9n\u00e9rale\" \/>\n<meta property=\"og:description\" content=\"cours de maths sur l&#039;arithm\u00e9tique en seconde g\u00e9n\u00e9rale : multiple et diviseur, PPCM et PGCD, nombres premiers etc..\" \/>\n<meta property=\"og:url\" content=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-arithmetique-seconde\/\" \/>\n<meta property=\"og:site_name\" content=\"Groupe R\u00e9ussite\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/GroupeReussiteOfficiel\/\" \/>\n<meta property=\"article:modified_time\" content=\"2024-02-29T18:24:19+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/uploads\/2026\/05\/logo-groupe-reussite-carre.png\" \/>\n\t<meta property=\"og:image:width\" content=\"170\" \/>\n\t<meta property=\"og:image:height\" content=\"180\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/png\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:site\" content=\"@GroupeReussite\" \/>\n<meta name=\"twitter:label1\" content=\"Dur\u00e9e de lecture estim\u00e9e\" \/>\n\t<meta name=\"twitter:data1\" content=\"8 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-arithmetique-seconde\/\",\"url\":\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-arithmetique-seconde\/\",\"name\":\"R\u00e9sum\u00e9 de cours et m\u00e9thodes : l'arithm\u00e9tique en seconde g\u00e9n\u00e9rale\",\"isPartOf\":{\"@id\":\"https:\/\/groupe-reussite.fr\/ressources\/#website\"},\"datePublished\":\"2021-01-20T15:43:44+00:00\",\"dateModified\":\"2024-02-29T18:24:19+00:00\",\"description\":\"cours de maths sur l'arithm\u00e9tique en seconde g\u00e9n\u00e9rale : multiple et diviseur, PPCM et PGCD, nombres premiers etc..\",\"breadcrumb\":{\"@id\":\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-arithmetique-seconde\/#breadcrumb\"},\"inLanguage\":\"fr-FR\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-arithmetique-seconde\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-arithmetique-seconde\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Accueil\",\"item\":\"https:\/\/groupe-reussite.fr\/ressources\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Cours en ligne arithm\u00e9tique seconde\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/groupe-reussite.fr\/ressources\/#website\",\"url\":\"https:\/\/groupe-reussite.fr\/ressources\/\",\"name\":\"Groupe R\u00e9ussite - Cours particuliers et stages de vacances\",\"description\":\"Stage et Cours particuliers maths, fran\u00e7ais, anglais, informatique, physique chimie\",\"publisher\":{\"@id\":\"https:\/\/groupe-reussite.fr\/ressources\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/groupe-reussite.fr\/ressources\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"fr-FR\"},{\"@type\":\"Organization\",\"@id\":\"https:\/\/groupe-reussite.fr\/ressources\/#organization\",\"name\":\"Groupe R\u00e9ussite - Cours particuliers et stages de vacances\",\"url\":\"https:\/\/groupe-reussite.fr\/ressources\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"fr-FR\",\"@id\":\"https:\/\/groupe-reussite.fr\/ressources\/#\/schema\/logo\/image\/\",\"url\":\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/uploads\/2026\/05\/logo-groupe-reussite-carre.png\",\"contentUrl\":\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/uploads\/2026\/05\/logo-groupe-reussite-carre.png\",\"width\":170,\"height\":180,\"caption\":\"Groupe R\u00e9ussite - Cours particuliers et stages de vacances\"},\"image\":{\"@id\":\"https:\/\/groupe-reussite.fr\/ressources\/#\/schema\/logo\/image\/\"},\"sameAs\":[\"https:\/\/www.facebook.com\/GroupeReussiteOfficiel\/\",\"https:\/\/twitter.com\/GroupeReussite\",\"https:\/\/www.youtube.com\/c\/GroupeReussite\",\"https:\/\/www.instagram.com\/groupe_reussite_officiel\/\",\"https:\/\/fr.linkedin.com\/company\/groupe-reussite\",\"https:\/\/www.tiktok.com\/@groupereussite\",\"https:\/\/fr.pinterest.com\/GroupeReussite\/\",\"https:\/\/www.reddit.com\/user\/Groupe-Reussite\/\"]}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"R\u00e9sum\u00e9 de cours et m\u00e9thodes : l'arithm\u00e9tique en seconde g\u00e9n\u00e9rale","description":"cours de maths sur l'arithm\u00e9tique en seconde g\u00e9n\u00e9rale : multiple et diviseur, PPCM et PGCD, nombres premiers etc..","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-arithmetique-seconde\/","og_locale":"fr_FR","og_type":"article","og_title":"R\u00e9sum\u00e9 de cours et m\u00e9thodes : l'arithm\u00e9tique en seconde g\u00e9n\u00e9rale","og_description":"cours de maths sur l'arithm\u00e9tique en seconde g\u00e9n\u00e9rale : multiple et diviseur, PPCM et PGCD, nombres premiers etc..","og_url":"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-arithmetique-seconde\/","og_site_name":"Groupe R\u00e9ussite","article_publisher":"https:\/\/www.facebook.com\/GroupeReussiteOfficiel\/","article_modified_time":"2024-02-29T18:24:19+00:00","og_image":[{"width":170,"height":180,"url":"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/uploads\/2026\/05\/logo-groupe-reussite-carre.png","type":"image\/png"}],"twitter_card":"summary_large_image","twitter_site":"@GroupeReussite","twitter_misc":{"Dur\u00e9e de lecture estim\u00e9e":"8 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-arithmetique-seconde\/","url":"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-arithmetique-seconde\/","name":"R\u00e9sum\u00e9 de cours et m\u00e9thodes : l'arithm\u00e9tique en seconde g\u00e9n\u00e9rale","isPartOf":{"@id":"https:\/\/groupe-reussite.fr\/ressources\/#website"},"datePublished":"2021-01-20T15:43:44+00:00","dateModified":"2024-02-29T18:24:19+00:00","description":"cours de maths sur l'arithm\u00e9tique en seconde g\u00e9n\u00e9rale : multiple et diviseur, PPCM et PGCD, nombres premiers etc..","breadcrumb":{"@id":"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-arithmetique-seconde\/#breadcrumb"},"inLanguage":"fr-FR","potentialAction":[{"@type":"ReadAction","target":["https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-arithmetique-seconde\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-arithmetique-seconde\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Accueil","item":"https:\/\/groupe-reussite.fr\/ressources\/"},{"@type":"ListItem","position":2,"name":"Cours en ligne arithm\u00e9tique seconde"}]},{"@type":"WebSite","@id":"https:\/\/groupe-reussite.fr\/ressources\/#website","url":"https:\/\/groupe-reussite.fr\/ressources\/","name":"Groupe R\u00e9ussite - Cours particuliers et stages de vacances","description":"Stage et Cours particuliers maths, fran\u00e7ais, anglais, informatique, physique chimie","publisher":{"@id":"https:\/\/groupe-reussite.fr\/ressources\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/groupe-reussite.fr\/ressources\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"fr-FR"},{"@type":"Organization","@id":"https:\/\/groupe-reussite.fr\/ressources\/#organization","name":"Groupe R\u00e9ussite - Cours particuliers et stages de vacances","url":"https:\/\/groupe-reussite.fr\/ressources\/","logo":{"@type":"ImageObject","inLanguage":"fr-FR","@id":"https:\/\/groupe-reussite.fr\/ressources\/#\/schema\/logo\/image\/","url":"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/uploads\/2026\/05\/logo-groupe-reussite-carre.png","contentUrl":"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/uploads\/2026\/05\/logo-groupe-reussite-carre.png","width":170,"height":180,"caption":"Groupe R\u00e9ussite - Cours particuliers et stages de vacances"},"image":{"@id":"https:\/\/groupe-reussite.fr\/ressources\/#\/schema\/logo\/image\/"},"sameAs":["https:\/\/www.facebook.com\/GroupeReussiteOfficiel\/","https:\/\/twitter.com\/GroupeReussite","https:\/\/www.youtube.com\/c\/GroupeReussite","https:\/\/www.instagram.com\/groupe_reussite_officiel\/","https:\/\/fr.linkedin.com\/company\/groupe-reussite","https:\/\/www.tiktok.com\/@groupereussite","https:\/\/fr.pinterest.com\/GroupeReussite\/","https:\/\/www.reddit.com\/user\/Groupe-Reussite\/"]}]}},"_links":{"self":[{"href":"https:\/\/groupe-reussite.fr\/ressources\/wp-json\/wp\/v2\/pages\/85316"}],"collection":[{"href":"https:\/\/groupe-reussite.fr\/ressources\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/groupe-reussite.fr\/ressources\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/groupe-reussite.fr\/ressources\/wp-json\/wp\/v2\/users\/6"}],"replies":[{"embeddable":true,"href":"https:\/\/groupe-reussite.fr\/ressources\/wp-json\/wp\/v2\/comments?post=85316"}],"version-history":[{"count":4,"href":"https:\/\/groupe-reussite.fr\/ressources\/wp-json\/wp\/v2\/pages\/85316\/revisions"}],"predecessor-version":[{"id":203565,"href":"https:\/\/groupe-reussite.fr\/ressources\/wp-json\/wp\/v2\/pages\/85316\/revisions\/203565"}],"wp:attachment":[{"href":"https:\/\/groupe-reussite.fr\/ressources\/wp-json\/wp\/v2\/media?parent=85316"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}