{"id":54039,"date":"2020-06-12T12:46:11","date_gmt":"2020-06-12T11:46:11","guid":{"rendered":"https:\/\/groupe-reussite.fr\/?page_id=54039"},"modified":"2022-07-27T10:41:17","modified_gmt":"2022-07-27T09:41:17","slug":"cours-en-ligne-arithmetique","status":"publish","type":"page","link":"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-arithmetique\/","title":{"rendered":"Cours arithm\u00e9tique"},"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<p style=\"text-align: justify;\">\t\t<div data-elementor-type=\"page\" data-elementor-id=\"86176\" class=\"elementor elementor-86176\">\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-6f9fb2b3 elementor-section-content-bottom elementor-section-boxed elementor-section-height-default elementor-section-height-default ae-bg-gallery-type-default\" data-id=\"6f9fb2b3\" data-element_type=\"section\">\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-5032621c sticky_badeau_colone strick_col ae-bg-gallery-type-default\" data-id=\"5032621c\" data-element_type=\"column\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\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<section class=\"has_ae_slider elementor-section elementor-top-section elementor-element elementor-element-611bd75f elementor-section-boxed elementor-section-height-default elementor-section-height-default ae-bg-gallery-type-default\" data-id=\"611bd75f\" data-element_type=\"section\">\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-55718945 strick_col ae-bg-gallery-type-default\" data-id=\"55718945\" 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-5940f45c elementor-widget elementor-widget-heading\" data-id=\"5940f45c\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<p class=\"elementor-heading-title elementor-size-default\"><a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-tage-mage\/\">Cours en ligne Tage Mage <\/a><\/p>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-f9bc725 elementor-widget elementor-widget-heading\" data-id=\"f9bc725\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<p class=\"elementor-heading-title elementor-size-default\">Chapitres du sous-test 2 du Tage Mage<\/p>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-56c02cf0 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"56c02cf0\" 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\/ressources\/cours-en-ligne-fractions\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\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\">Fractions<\/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-390da5ff elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"390da5ff\" 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\/ressources\/cours-en-ligne-pourcentages\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\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\">Pourcentages<\/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-da8d658 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"da8d658\" 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\/ressources\/cours-en-ligne-exercices-corriges-algebre\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\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\">Alg\u00e8bre<\/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-490ac2aa elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"490ac2aa\" 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\/ressources\/cours-en-ligne-figures-geometriques\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\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\">G\u00e9om\u00e9trie<\/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-3fd40310 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"3fd40310\" 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\/ressources\/cours-en-ligne-vitesse\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\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\">Vitesse<\/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-6edf1c7e elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"6edf1c7e\" 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\/ressources\/cours-en-ligne-arithmetique\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\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\">Arithm\u00e9tique<\/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-4f2c805 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"4f2c805\" 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\/ressources\/cours-en-ligne-puissances\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\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\">Puissances<\/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-447b658 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"447b658\" 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\/ressources\/cours-en-ligne-regle-de-trois\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\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\">Proportionnalit\u00e9<\/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-53863aa elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"53863aa\" 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\/ressources\/cours-en-ligne-denombrement\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\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\">D\u00e9nombrement<\/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-11741389 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"11741389\" 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\/ressources\/cours-en-ligne-probabilites\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\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\">Probabilit\u00e9s<\/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-6ace8ace elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"6ace8ace\" 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\/ressources\/cours-en-ligne-moyenne-arithmetique-moyenne-ponderee\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\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\">Moyenne<\/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-13f1db2f elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"13f1db2f\" 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\/ressources\/cours-en-ligne-theoreme-de-pythagore\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\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\">Th\u00e9or\u00e8me de Pythagore<\/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-10d04684 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"10d04684\" 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\/ressources\/cours-en-ligne-theoreme-de-thales\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\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\">Th\u00e9or\u00e8me de Thal\u00e8s<\/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-691a3a8a elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"691a3a8a\" 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\/ressources\/cours-en-ligne-racines-carrees\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\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\">Racines Carr\u00e9es<\/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-2a5f7bd6 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"2a5f7bd6\" 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\/nous-contacter\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\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\">CONTACTEZ-NOUS<\/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\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\" style=\"color: #000000; font-family: Lato, sans-serif; text-align: justify;\">\n<h1 class=\"Latex_page_title\">Cours arithm\u00e9tique : nombres premiers, divisibilit\u00e9, PPCM &amp; PGCD<\/h1>\n<\/div>\n<p class=\"colone_latex_ancres\" style=\"color: #000000; font-family: Lato, sans-serif; text-align: center;\"><a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-arithmetique\/\">R\u00e9sum\u00e9 de cours<\/a> <a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-exercices-corriges-arithmetique\/\">Exercices et corrig\u00e9s<\/a><\/p>\n<p class=\"colone_latex_ancres\" style=\"color: #000000; font-family: Lato, sans-serif; text-align: center;\"><a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-tage-mage\/\">Cours en ligne du Tage Mage<\/a><\/p>\n<p style=\"text-align: justify;\">Les programmes de maths au coll\u00e8ge et au lyc\u00e9e \u00e0 partir de l&rsquo;ann\u00e9e de troisi\u00e8me se suivent avec souvent les m\u00eames chapitres qui reviennent et qui sont approfondis chaque ann\u00e9e. C&rsquo;est le cas du chapitre sur l&rsquo;arithm\u00e9tique qui au programme de maths de 3\u00e8me mais \u00e9galement au programme en seconde et en terminale. Ce chapitre important est tr\u00e8s utile pour pr\u00e9parer le Tage Mage et le Score IAE Message \u00e9galement. Ainsi connaitre les <strong>crit\u00e8res de divisibilit\u00e9<\/strong> d&rsquo;un nombre, les propri\u00e9t\u00e9s d&rsquo;un <strong>nombre premier<\/strong> et savoir utiliser le <strong>PPCM et PGCD<\/strong> est aussi n\u00e9cessaire en vue de la pr\u00e9paration au baccalaur\u00e9at.<\/p>\n<h2 style=\"text-align: justify;\">1. D\u00e9finition divisibilit\u00e9<\/h2>\n<p class=\"p1\" style=\"text-align: justify;\">D\u00e9finition et Vocabulaire\u00a0:<\/p>\n<p class=\"p1\" style=\"text-align: justify;\">Si <i>a<\/i>, <i>b<\/i> et <i>k<\/i> sont trois entiers relatifs tels que <i>a<\/i> = <i>b<\/i> <b>\u00d7<\/b><i> k<\/i>, alors\u00a0:<\/p>\n<ul class=\"ul1\" style=\"text-align: justify;\">\n<li class=\"li1\"><i>b<\/i> est un diviseur de <i>a<\/i>.<\/li>\n<li class=\"li1\"><i>k<\/i> est un diviseur de <i>a<\/i>.<\/li>\n<li class=\"li1\"><i>a<\/i> est un multiple de <i>b<\/i> (et de <i>k<\/i>).<\/li>\n<\/ul>\n<p class=\"p1\" style=\"text-align: justify;\">Autrement dit\u00a0:<\/p>\n<ul class=\"ul1\" style=\"text-align: justify;\">\n<li class=\"li1\">7 est un <strong>diviseur<\/strong> de 35. En effet : \u00ab lorsque l\u2019on divise 35 par 7, \u00e7a tombe juste \u00bb.<\/li>\n<li class=\"li1\">36 est un <strong>multiple<\/strong> de 12 signifie : \u00ab 36 est dans la table de multiplication de 12 \u00bb.<\/li>\n<\/ul>\n<p class=\"p1\" style=\"text-align: justify;\">Un nombre (autre que 1) admet toujours au moins 2 diviseurs\u00a0: 1 et lui m\u00eame.<\/p>\n<p>&nbsp;<\/p>\n\t\t<div data-elementor-type=\"section\" data-elementor-id=\"84983\" class=\"elementor elementor-84983\">\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-51d9c4d 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=\"51d9c4d\" 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-610eeeb9 ae-bg-gallery-type-default\" data-id=\"610eeeb9\" 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-5bf69eb8 elementor-widget elementor-widget-heading\" data-id=\"5bf69eb8\" 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\">COURS DE MATHS<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-49568da4 elementor-widget elementor-widget-heading\" data-id=\"49568da4\" 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\">Les meilleurs professeurs particuliers<\/h4>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-1eb9e0cb elementor-widget elementor-widget-heading\" data-id=\"1eb9e0cb\" 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\">Pour progresser et r\u00e9ussir<\/h4>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-15c3e28d elementor-align-left elementor-mobile-align-center elementor-widget elementor-widget-button\" data-id=\"15c3e28d\" 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 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-1a5c10e7 elementor-widget elementor-widget-text-editor\" data-id=\"1a5c10e7\" 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-6913d4fe ae-bg-gallery-type-default\" data-id=\"6913d4fe\" 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 class=\"p1\" style=\"text-align: justify;\"><b>2. Nombres premiers<\/b><\/h2>\n<p class=\"p1\" style=\"text-align: justify;\">Un <strong>nombre premier<\/strong> est un nombre qui admet exactement 2 diviseurs\u00a0: 1 et lui m\u00eame.<\/p>\n<p class=\"p1\" style=\"text-align: justify;\">Autre fa\u00e7on de comprendre la d\u00e9finition : un nombre est premier si<\/p>\n<ul class=\"ul1\" style=\"text-align: justify;\">\n<li class=\"li1\">sa seule d\u00e9composition est \u00ab 1 <b>\u00d7<\/b> <i>lui m\u00eame\u00a0<\/i>\u00bb.<\/li>\n<li class=\"li1\">on ne peut le diviser par aucun autre nombre (sauf 1 et lui m\u00eame)<\/li>\n<\/ul>\n<p class=\"p1\" style=\"text-align: justify;\"><strong>1 n\u2019est pas premier<\/strong> (un seul diviseur).<\/p>\n<p style=\"text-align: justify;\"><strong>Liste des nombres premiers<\/strong> :<\/p>\n<p style=\"text-align: justify;\">2 &#8211; 3\u00a0 &#8211; 7 &#8211; 11 &#8211; 13 &#8211; 17 &#8211; 19 &#8211; 23 &#8211; 29 &#8211; 31 &#8211; 37 &#8211; 41 &#8211; 43 &#8211; 47 &#8211; 53 &#8211; 59 &#8211; 61 &#8211; 67 &#8211; 71 &#8211; 73 &#8211; 79 &#8211; 83 &#8211; 89 &#8211; 97 &#8211; 101 etc.<\/p>\n<p style=\"text-align: justify;\">2 est le seul nombre pair et premier.<\/p>\n<h2 style=\"text-align: justify;\">3. Crit\u00e8res de divisibilit\u00e9<\/h2>\n<ul class=\"ul1\" style=\"text-align: justify;\">\n<li class=\"li1\">Un nombre est divisible par 3 ou multiple de 3 si la somme de ses chiffres et dans la table de 3.\n<ul class=\"ul1\">\n<li class=\"li1\">Exemple 2751. On a 2 + 7 + 5 + 1 = 15, multiple de 3 donc 2751 est lui-m\u00eame multiple de 3.<\/li>\n<\/ul>\n<\/li>\n<li class=\"li1\">Un nombre est divisible par 4 si ses deux derniers chiffres forment un multiple de 4.\n<ul class=\"ul1\">\n<li class=\"li1\">Exemple : 5312 est un multiple de 4 car les 2 derniers chiffres 12 sont un multiple de 4.<\/li>\n<\/ul>\n<\/li>\n<li class=\"li1\">Un nombre est divisible par 5 s\u2019il se termine par 0 ou par 5.\n<ul class=\"ul1\">\n<li>Exemple : 1230 est divisible par 5.<\/li>\n<\/ul>\n<\/li>\n<li class=\"li1\">Un nombre est divisible par 9 ou multiple de 9 si la somme de ses chiffres et dans la table de 9.\n<ul class=\"ul1\">\n<li class=\"li1\">Exemple 2751. On a 2 + 7 + 5 + 1 = 15, n\u2019est pas un multiple de 9.<\/li>\n<\/ul>\n<\/li>\n<li class=\"li1\">Un nombre est divisible par 6 s\u2019il est divisible par <strong>3 et par 2. <\/strong>Autrement dit, s&rsquo;il est pair et que la somme de ses chiffres est un multiple de 3\n<ul class=\"ul1\">\n<li>Exemple : 72 est divisible par 6<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p style=\"text-align: justify;\"><strong>A retenir sur les crit\u00e8res de divisibilit\u00e9 :\u00a0<\/strong><\/p>\n<ul style=\"text-align: justify;\">\n<li>Si N est un <strong>multiple<\/strong> de 12, alors c&rsquo;est un <em>multiple<\/em> de 3 et 4<\/li>\n<li>Si X est un <strong>diviseur<\/strong> de 15, alors c&rsquo;est un <em>diviseur<\/em> de 30 ou 45<\/li>\n<\/ul>\n<p style=\"text-align: justify;\"><strong>Attention :\u00a0<\/strong><\/p>\n<ul style=\"text-align: justify;\">\n<li>Si Y est un <strong>diviseur<\/strong> de 60, Y n&rsquo;est pas n\u00e9cessairement un <em>diviseur<\/em> de 15.<\/li>\n<li>Si A est un <strong>multiple<\/strong> de 5, A n&rsquo;est pas n\u00e9cessairement un <em>multiple<\/em> de 15.<\/li>\n<\/ul>\n<h2 style=\"text-align: justify;\">4. PPCM<\/h2>\n<p style=\"text-align: justify;\">PPCM : Plus Petit Commun Multiple<\/p>\n<p class=\"p1\" style=\"text-align: justify;\"><b><i>Question type PPCM au Tage Mage :<\/i><\/b><\/p>\n<p class=\"p2\" style=\"text-align: justify;\">Sarah et Jessica sont \u00e0 la biblioth\u00e8que et pr\u00e9parent leur bac de math\u00e9matiques. Sarah fait un exercice complet toutes les 24 minutes tandis que pour Jessica, il lui faut 40 minutes. Elles d\u00e9cident de prendre une pause uniquement si elles ont toutes les deux fini un exercice. Sachant qu\u2019elles commencent leur r\u00e9vision \u00e0 9h, \u00e0 quelle heure pourront-elles prendre leur premi\u00e8re pause ?<\/p>\n<p class=\"p1\" style=\"text-align: justify;\">A) 9h40<\/p>\n<p class=\"p1\" style=\"text-align: justify;\">B) 10h12<\/p>\n<p class=\"p1\" style=\"text-align: justify;\">C) 10h20<\/p>\n<p class=\"p1\" style=\"text-align: justify;\">D) 10h40<\/p>\n<p class=\"p1\" style=\"text-align: justify;\">E) 11h<\/p>\n<p class=\"p1\" style=\"text-align: justify;\"><b><i>R\u00e9solution de l&rsquo;exemple sur les PPCM :<\/i><\/b><\/p>\n<p class=\"p2\" style=\"text-align: justify;\">Il faut ici trouver le plus petit multiple de 40 min et 24 min pour qu\u2019elles aient toutes deux fini un certain nombre d\u2019exercices (pas le m\u00eame nombre d&rsquo;exercices) et qu&rsquo;elles puissent toutes deux prendre la pause. Ces <a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-series-lettres-nombres\/\">nombres<\/a> n\u2019\u00e9tant pas si petits, on utilise la d\u00e9composition en facteurs premiers ; on ne veut que des nombres premiers :<\/p>\n<p class=\"p1\" style=\"text-align: justify;\">24 = 6\u00d74 = 3\u00d72\u00d72\u00d72 = 2<sup>3<\/sup>\u00d73<\/p>\n<p class=\"p1\" style=\"text-align: justify;\">40 = 8\u00d75 = 2<sup>3<\/sup>\u00d75<\/p>\n<p class=\"p1\" style=\"text-align: justify;\">Pour d\u00e9terminer le <strong>PPCM<\/strong>, on prend les plus grandes <a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-puissances\/\">puissances<\/a> de chacun des facteurs, ce qui donne\u00a0: 2<sup>3<\/sup>\u00d73\u00d75 = 120. Il faudra donc attendre 120 min soit 2h pour qu\u2019elles soient toutes les deux \u00e0 la fin d\u2019un exercice, soit \u00e0 11h.<\/p>\n<p style=\"text-align: justify;\">Pour <strong>d\u00e9terminer le PPCM entre deux nombres<\/strong> :<\/p>\n<ol style=\"text-align: justify;\">\n<li>On les d\u00e9compose en facteurs premiers<\/li>\n<li>Puis on prend les plus grandes puissances pr\u00e9sentes<\/li>\n<\/ol>\n<p>&nbsp;<\/p>\n\t\t<div data-elementor-type=\"section\" data-elementor-id=\"127774\" class=\"elementor elementor-127774\">\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-5a7b6a2a 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=\"5a7b6a2a\" 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-749af387 ae-bg-gallery-type-default\" data-id=\"749af387\" 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-1b4ed465 elementor-widget elementor-widget-heading\" data-id=\"1b4ed465\" 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\">COURS PARTICULIERS EN LIGNE<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-16d47760 elementor-widget elementor-widget-heading\" data-id=\"16d47760\" 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\">Nous avons s\u00e9lectionn\u00e9 pour vous les meilleurs professeurs particuliers.<\/h4>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-21a162bf elementor-widget elementor-widget-heading\" data-id=\"21a162bf\" 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\">POUR ACC\u00c9L\u00c9RER MA PROGRESSION<\/h4>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-5600477e elementor-align-left elementor-mobile-align-center elementor-widget elementor-widget-button\" data-id=\"5600477e\" 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-en-ligne\/toutes-matieres\/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 particuliers en ligne<\/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-1c7a7876 elementor-widget elementor-widget-text-editor\" data-id=\"1c7a7876\" 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-2aa12288 ae-bg-gallery-type-default\" data-id=\"2aa12288\" 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 style=\"text-align: justify;\">5. PGCD<\/h2>\n<p style=\"text-align: justify;\">PGCD : Plus Grand Commun Diviseur<\/p>\n<p class=\"p1\" style=\"text-align: justify;\"><b><i>Question type PGCD au Tage Mage.<\/i><\/b><\/p>\n<p class=\"p2\" style=\"text-align: justify;\">Un professeur d\u2019EPS souhaite faire des \u00e9quipes pour un tournoi incluant plusieurs disciplines sportives. Il y a 108 gar\u00e7ons et 84 filles. Les \u00e9quipes doivent \u00eatre identiques entre elles, m\u00eame nombre de filles et de gar\u00e7ons par \u00e9quipe et il doit utiliser tous ses \u00e9l\u00e8ves. Combien d\u2019\u00e9quipes au maximum pourra-t-il alors composer\u00a0?<\/p>\n<p class=\"p1\" style=\"text-align: justify;\">A) 4 \u00e9quipes<\/p>\n<p class=\"p1\" style=\"text-align: justify;\">B) 6 \u00e9quipes<\/p>\n<p class=\"p1\" style=\"text-align: justify;\">C) 12 \u00e9quipes<\/p>\n<p class=\"p1\" style=\"text-align: justify;\">D) 18 \u00e9quipes<\/p>\n<p class=\"p1\" style=\"text-align: justify;\">E) 84 \u00e9quipes<\/p>\n<p class=\"p1\" style=\"text-align: justify;\"><b><i>R\u00e9solution de l&rsquo;exemple sur les PGCD :<\/i><\/b><\/p>\n<p class=\"p1\" style=\"text-align: justify;\">Si le prof fait 2 \u00e9quipes, il y aura 54 gar\u00e7ons et 42 filles par \u00e9quipes. Ces deux \u00e9quipes sont bien identiques entre elles mais ce n\u2019est \u00e9videmment pas le nombre maximum d\u2019\u00e9quipes possibles.<\/p>\n<p class=\"p1\" style=\"text-align: justify;\">Le nombre d\u2019\u00e9quipes doit \u00eatre un <b>diviseur<\/b> de 108 et de 84, sinon il restera des \u00e9l\u00e8ves sans \u00e9quipe. De plus, on veut un maximum d\u2019\u00e9quipes, on cherche donc le plus grand de ces diviseurs communs, le <strong>PGCD<\/strong>. On d\u00e9compose ces deux nombres en facteurs premiers\u00a0:<\/p>\n<p class=\"p1\" style=\"text-align: justify;\">108 = 2\u00d754 = 2\u00d79\u00d76 = 2\u00d73\u00d73\u00d72\u00d73 = 2<sup>2<\/sup>\u00d73<sup>3<\/sup><\/p>\n<p class=\"p1\" style=\"text-align: justify;\">84 = 12\u00d77 = 2\u00d72\u00d73\u00d77 = 2<sup>2<\/sup>\u00d73\u00d77<\/p>\n<p class=\"p1\" style=\"text-align: justify;\">Pour d\u00e9terminer le <strong>PGCD<\/strong> on doit prendre les plus <b>petites<\/b> puissances des facteurs, on prend ce qu\u2019il y a en commun entre eux, ce qui donne\u00a0: 2<sup>2<\/sup>\u00d73 = 12. Le professeur pourra donc faire 12 \u00e9quipes. Et la composition de chacune sera\u00a0: 9 gar\u00e7ons (9\u00d712 = 108) et 7 filles (7\u00d712 = 84).<\/p>\n<p style=\"text-align: justify;\">Pour <strong>d\u00e9terminer le PGCD entre deux nombres<\/strong> :<\/p>\n<ol style=\"text-align: justify;\">\n<li>On les d\u00e9compose en facteurs premiers<\/li>\n<li>Puis on prend les plus petites puissances pr\u00e9sentes<\/li>\n<\/ol>\n<p style=\"text-align: justify;\">Comme tout examen, le Tage Mage doit \u00eatre pr\u00e9par\u00e9 pour obtenir le meilleur score possible. Les cours en ligne du sous-test 2 suivants, vous permettent ainsi de pouvoir faire une pr\u00e9paration compl\u00e8te et efficace depuis chez vous :<\/p>\n<ul>\n<li style=\"text-align: justify;\"><a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-puissances\/\">les puissances<\/a><\/li>\n<li style=\"text-align: justify;\"><a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-regle-de-trois\/\">la proportionnalit\u00e9<\/a><\/li>\n<li style=\"text-align: justify;\"><a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-denombrement\/\">le d\u00e9nombrement<\/a><\/li>\n<li style=\"text-align: justify;\"><a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-probabilites\/\">les probabilit\u00e9s<\/a><\/li>\n<li><a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-moyenne-arithmetique-moyenne-ponderee\/\">les moyennes<\/a><\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Cours arithm\u00e9tique : nombres premiers, divisibilit\u00e9, PPCM &amp; PGCD R\u00e9sum\u00e9 de cours Exercices et corrig\u00e9s Cours en ligne du Tage Mage Les programmes de maths au coll\u00e8ge et au lyc\u00e9e \u00e0 partir de l&rsquo;ann\u00e9e de troisi\u00e8me se suivent avec souvent les m\u00eames chapitres qui reviennent et qui sont approfondis chaque ann\u00e9e. C&rsquo;est le cas du [&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>Arithmetique: divisibilit\u00e9, nombres premiers, PPCM, PGCD<\/title>\n<meta name=\"description\" content=\"D\u00e9couvrez un cours complet d&#039;arithmetique qui aborde les crit\u00e8res de divisibilit\u00e9, les nombres premiers le PPCM et le PGCD.\" \/>\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\/\" \/>\n<meta property=\"og:locale\" content=\"fr_FR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Arithmetique: divisibilit\u00e9, nombres premiers, PPCM, PGCD\" \/>\n<meta property=\"og:description\" content=\"D\u00e9couvrez un cours complet d&#039;arithmetique qui aborde les crit\u00e8res de divisibilit\u00e9, les nombres premiers le PPCM et le PGCD.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-arithmetique\/\" \/>\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=\"2022-07-27T09:41:17+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=\"6 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\/\",\"url\":\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-arithmetique\/\",\"name\":\"Arithmetique: divisibilit\u00e9, nombres premiers, PPCM, PGCD\",\"isPartOf\":{\"@id\":\"https:\/\/groupe-reussite.fr\/ressources\/#website\"},\"datePublished\":\"2020-06-12T11:46:11+00:00\",\"dateModified\":\"2022-07-27T09:41:17+00:00\",\"description\":\"D\u00e9couvrez un cours complet d'arithmetique qui aborde les crit\u00e8res de divisibilit\u00e9, les nombres premiers le PPCM et le PGCD.\",\"breadcrumb\":{\"@id\":\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-arithmetique\/#breadcrumb\"},\"inLanguage\":\"fr-FR\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-arithmetique\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-arithmetique\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Accueil\",\"item\":\"https:\/\/groupe-reussite.fr\/ressources\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Cours arithm\u00e9tique\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/groupe-reussite.fr\/ressources\/#website\",\"url\":\"https:\/\/groupe-reussite.fr\/ressources\/\",\"name\":\"Groupe R\u00e9ussite - 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