{"id":1888,"date":"2023-11-22T20:30:14","date_gmt":"2023-11-22T19:30:14","guid":{"rendered":"http:\/\/localhost:8080\/maxblog\/?p=1888"},"modified":"2023-11-22T23:56:00","modified_gmt":"2023-11-22T22:56:00","slug":"utiliser-les-notions-de-multiple-diviseur-et-de-nombre-premier","status":"publish","type":"post","link":"https:\/\/www.maxdecours.com\/maxblog\/utiliser-les-notions-de-multiple-diviseur-et-de-nombre-premier\/","title":{"rendered":"Utiliser les notions de multiple, diviseur et de nombre premier"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"1888\" class=\"elementor elementor-1888\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-7d71a4a elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"7d71a4a\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-389cd7d\" data-id=\"389cd7d\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-a8169f1 elementor-widget elementor-widget-spacer\" data-id=\"a8169f1\" data-element_type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-7643655 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"7643655\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-f297427\" data-id=\"f297427\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-361d80f elementor-widget elementor-widget-heading\" data-id=\"361d80f\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-heading-title elementor-size-xl\">Utiliser les notions de multiple, diviseur et de nombre premier<\/div>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-c2bda19 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"c2bda19\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-d178bc4\" data-id=\"d178bc4\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-de06178 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"de06178\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-cc24190\" data-id=\"cc24190\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-b7c611b elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"b7c611b\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-9a7e2c2\" data-id=\"9a7e2c2\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-fffe349 nc-justify-text elementor-widget elementor-widget-text-editor\" data-id=\"fffe349\" 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\t<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_82_2 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-1'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/www.maxdecours.com\/maxblog\/utiliser-les-notions-de-multiple-diviseur-et-de-nombre-premier\/#Introduction\" >Introduction<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-1'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/www.maxdecours.com\/maxblog\/utiliser-les-notions-de-multiple-diviseur-et-de-nombre-premier\/#Cours\" >Cours<\/a><ul class='ez-toc-list-level-2' ><li class='ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/www.maxdecours.com\/maxblog\/utiliser-les-notions-de-multiple-diviseur-et-de-nombre-premier\/#1_Notations_%E2%84%95_et_%E2%84%A4\" >1. Notations \u2115 et \u2124<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/www.maxdecours.com\/maxblog\/utiliser-les-notions-de-multiple-diviseur-et-de-nombre-premier\/#2_Definition_des_notions\" >2. D\u00e9finition des notions<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-1'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/www.maxdecours.com\/maxblog\/utiliser-les-notions-de-multiple-diviseur-et-de-nombre-premier\/#Methodes\" >M\u00e9thodes&nbsp;:<\/a><ul class='ez-toc-list-level-2' ><li class='ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/www.maxdecours.com\/maxblog\/utiliser-les-notions-de-multiple-diviseur-et-de-nombre-premier\/#1_Modeliser_et_resoudre_des_problemes\" >1. Mod\u00e9liser et r\u00e9soudre des probl\u00e8mes<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/www.maxdecours.com\/maxblog\/utiliser-les-notions-de-multiple-diviseur-et-de-nombre-premier\/#2_Presenter_les_resultats_fractionnaires_sous_forme_irreductible\" >2. Pr\u00e9senter les r\u00e9sultats fractionnaires sous forme irr\u00e9ductible :<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h1><span class=\"ez-toc-section\" id=\"Introduction\"><\/span>Introduction<span class=\"ez-toc-section-end\"><\/span><\/h1>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\">La compr\u00e9hension des notions de multiple et de diviseur est\nfondamentale en math\u00e9matiques. Ces concepts nous permettent de classer et de\nmanipuler les nombres de diff\u00e9rentes mani\u00e8res, facilitant ainsi la r\u00e9solution\nde probl\u00e8mes plus complexes. Les nombres pairs et impairs sont des cas\nparticuliers de ces concepts et sont fr\u00e9quemment utilis\u00e9s dans de nombreux\ndomaines des math\u00e9matiques et de la science en g\u00e9n\u00e9ral.<\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<h1><span class=\"ez-toc-section\" id=\"Cours\"><\/span>Cours<span class=\"ez-toc-section-end\"><\/span><\/h1>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<h2><span class=\"ez-toc-section\" id=\"1_Notations_%E2%84%95_et_%E2%84%A4\"><\/span>1. Notations <span style=\"font-family:&quot;Cambria Math&quot;,serif;mso-bidi-font-family:\n&quot;Cambria Math&quot;\">\u2115<\/span> et <span style=\"font-family:&quot;Cambria Math&quot;,serif;\nmso-bidi-font-family:&quot;Cambria Math&quot;\">\u2124<\/span><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\">Avant de plonger dans les notions de multiple, de diviseur\net de nombre premier, commen\u00e7ons par comprendre les notations <span style=\"font-family:&quot;Cambria Math&quot;,serif;mso-bidi-font-family:&quot;Cambria Math&quot;\">\u2115<\/span>\net <span style=\"font-family:&quot;Cambria Math&quot;,serif;mso-bidi-font-family:&quot;Cambria Math&quot;\">\u2124<\/span>.<\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\">&#8211; <b><span style=\"font-family:&quot;Cambria Math&quot;,serif;\nmso-bidi-font-family:&quot;Cambria Math&quot;\">\u2115<\/span><\/b> : L&rsquo;ensemble des nombres\nentiers naturels est not\u00e9 <span style=\"font-family:&quot;Cambria Math&quot;,serif;\nmso-bidi-font-family:&quot;Cambria Math&quot;\">\u2115<\/span>. Il regroupe tous les entiers\nnon-n\u00e9gatifs, \u00e0 partir de 0 et s&rsquo;\u00e9tendant \u00e0 l&rsquo;infini : <span class=\"katex-eq\" data-katex-display=\"false\">\\mathbb{Z} = \\{0,\n1, 2, 3, 4, 5, &#8230;\\}<\/span><\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\">&#8211; <b><span style=\"font-family:&quot;Cambria Math&quot;,serif;\nmso-bidi-font-family:&quot;Cambria Math&quot;\">\u2124<\/span><\/b> : L&rsquo;ensemble des nombres\nentiers relatifs est not\u00e9 <span style=\"font-family:&quot;Cambria Math&quot;,serif;\nmso-bidi-font-family:&quot;Cambria Math&quot;\">\u2124<\/span>. Il comprend \u00e0 la fois les\nentiers positifs, les entiers n\u00e9gatifs et z\u00e9ro : <span class=\"katex-eq\" data-katex-display=\"false\">\\mathbb{N} = \\{&#8230;, -3,\n-2, -1, 0, 1, 2, 3, &#8230;\\}<\/span><\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<h2><span class=\"ez-toc-section\" id=\"2_Definition_des_notions\"><\/span>2. D\u00e9finition des notions<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\"><b>2.1 Multiple<\/b><\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\">Un nombre <span class=\"katex-eq\" data-katex-display=\"false\">a<\/span> est dit multiple d&rsquo;un autre\nnombre <span class=\"katex-eq\" data-katex-display=\"false\">b<\/span> (avec <span class=\"katex-eq\" data-katex-display=\"false\">b \\neq 0<\/span>), si <span class=\"katex-eq\" data-katex-display=\"false\">a<\/span> est\nle r\u00e9sultat de la multiplication de <span class=\"katex-eq\" data-katex-display=\"false\">b<\/span> par un entier.\nMath\u00e9matiquement, on \u00e9crit <span class=\"katex-eq\" data-katex-display=\"false\">a<\/span> est multiple de <span class=\"katex-eq\" data-katex-display=\"false\">b<\/span>\nsi, et seulement si, il existe un entier <span class=\"katex-eq\" data-katex-display=\"false\">k<\/span> tel que <span class=\"katex-eq\" data-katex-display=\"false\">a = b\n\\times k<\/span>. Par exemple, 12 est un multiple de 4 car <span class=\"katex-eq\" data-katex-display=\"false\">12 = 4 \\times\n3<\/span>.<\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\"><b>2.2 Diviseur<\/b><\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\">Un nombre <span class=\"katex-eq\" data-katex-display=\"false\">a<\/span> est dit diviseur d&rsquo;un autre\nnombre <span class=\"katex-eq\" data-katex-display=\"false\">b<\/span>, si la division de <span class=\"katex-eq\" data-katex-display=\"false\">b<\/span> par\n<span class=\"katex-eq\" data-katex-display=\"false\">a<\/span> donne un quotient qui est un entier. Math\u00e9matiquement, on\n\u00e9crit <span class=\"katex-eq\" data-katex-display=\"false\">a<\/span> est un diviseur de <span class=\"katex-eq\" data-katex-display=\"false\">b<\/span> si, et seulement si,\nil existe un entier <span class=\"katex-eq\" data-katex-display=\"false\">k<\/span> tel que <span class=\"katex-eq\" data-katex-display=\"false\">b = a \\times k<\/span>. Par\nexemple, 3 est un diviseur de 12 car <span class=\"katex-eq\" data-katex-display=\"false\">12 = 3 \\times 4<\/span>. <\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\"><b>2.3 Nombre pair et nombre impair<\/b><\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\">&#8211; <b>Nombre pair<\/b> : Un nombre entier <span class=\"katex-eq\" data-katex-display=\"false\">n<\/span> est\ndit pair si et seulement si <span class=\"katex-eq\" data-katex-display=\"false\">n<\/span> est divisible par 2, c&rsquo;est-\u00e0-dire\nqu&rsquo;il existe un entier <span class=\"katex-eq\" data-katex-display=\"false\">k<\/span> tel que <span class=\"katex-eq\" data-katex-display=\"false\">n = 2 \\times k<\/span>.\nPar exemple, 4, 6 et 8 sont des nombres pairs car ils sont respectivement\nmultiples de 2.<\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\">&#8211; <b>Nombre impair<\/b> : Un nombre entier <span class=\"katex-eq\" data-katex-display=\"false\">n<\/span>\nest dit impair si et seulement si <span class=\"katex-eq\" data-katex-display=\"false\">n<\/span> n&rsquo;est pas divisible par 2,\nc&rsquo;est-\u00e0-dire que, lorsqu&rsquo;on divise <span class=\"katex-eq\" data-katex-display=\"false\">n<\/span> par 2, le reste est 1.\nMath\u00e9matiquement, un nombre <span class=\"katex-eq\" data-katex-display=\"false\">n<\/span> est impair si <span class=\"katex-eq\" data-katex-display=\"false\">n = 2k +\n1<\/span> o\u00f9 <span class=\"katex-eq\" data-katex-display=\"false\">k<\/span> est un entier. Par exemple, 3, 5 et 7 sont des\nnombres impairs.<\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<h1><span class=\"ez-toc-section\" id=\"Methodes\"><\/span>M\u00e9thodes&nbsp;:<span class=\"ez-toc-section-end\"><\/span><\/h1>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<h2><span class=\"ez-toc-section\" id=\"1_Modeliser_et_resoudre_des_problemes\"><\/span>1. Mod\u00e9liser et r\u00e9soudre des probl\u00e8mes<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\"><b>1.1 Probl\u00e8mes li\u00e9s aux multiples et aux diviseurs :<\/b><\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\">Pour r\u00e9soudre des probl\u00e8mes li\u00e9s aux multiples et aux\ndiviseurs, vous pouvez suivre ces \u00e9tapes :<\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\">&#8211; <b>Identification<\/b> : D\u00e9terminez si le probl\u00e8me requiert\nla recherche de multiples ou de diviseurs.<br style=\"mso-special-character:\nline-break\">\n<br style=\"mso-special-character:line-break\">\n<\/p>\n\n<p class=\"MsoNormal\">&#8211; <b>Formulation d&rsquo;\u00e9quations<\/b> : Formulez des \u00e9quations bas\u00e9es\nsur les informations donn\u00e9es.<\/p>\n\n<p class=\"MsoNormal\"><br>\n&#8211; <b>R\u00e9solution<\/b> : R\u00e9solvez les \u00e9quations pour trouver la solution.<\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\"><b>Exemple<\/b> : Si un probl\u00e8me demande de trouver tous les\nmultiples de 5 entre 10 et 50, vous pouvez simplement lister ces multiples en\najoutant 5 \u00e0 chaque \u00e9tape, en commen\u00e7ant par le plus petit multiple dans la\nplage donn\u00e9e (10, 15, 20, &#8230;, 50).<\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\"><b>1.2. Probl\u00e8mes li\u00e9s aux nombres pairs et impairs :<\/b><\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\">Ces probl\u00e8mes sont souvent r\u00e9solus en utilisant la propri\u00e9t\u00e9\ndes nombres pairs (<span class=\"katex-eq\" data-katex-display=\"false\">2k<\/span>) et impairs (<span class=\"katex-eq\" data-katex-display=\"false\">2k+1<\/span>).<\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\"><b>Exemple<\/b> : Si un probl\u00e8me demande de trouver deux\nnombres cons\u00e9cutifs impairs dont la somme est 20, vous pouvez d\u00e9finir les\nnombres comme <span class=\"katex-eq\" data-katex-display=\"false\">2k+1<\/span> et <span class=\"katex-eq\" data-katex-display=\"false\">2k+3<\/span>, puis r\u00e9soudre l&rsquo;\u00e9quation\n<span class=\"katex-eq\" data-katex-display=\"false\">2k+1 + 2k+3 = 20<\/span>.<\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\"><b>1.3. Probl\u00e8mes li\u00e9s aux nombres premiers :<\/b><\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\">Pour r\u00e9soudre des probl\u00e8mes li\u00e9s aux nombres premiers,\nutilisez les propri\u00e9t\u00e9s des nombres premiers.<\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\">&#8211; <b>Identification<\/b> : Un nombre premier est un nombre\nnaturel sup\u00e9rieur \u00e0 1 qui n&rsquo;a pas d&rsquo;autres diviseurs que 1 et lui-m\u00eame.<\/p>\n\n<p class=\"MsoNormal\"><br>\n&#8211; <b>V\u00e9rification<\/b> : Pour v\u00e9rifier si un nombre est premier, vous pouvez le\ndiviser par tous les nombres inf\u00e9rieurs \u00e0 sa racine carr\u00e9e. Si aucune division\nne donne un quotient entier, alors le nombre est premier.<\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\"><b>Exemple<\/b> : Si vous devez trouver le plus petit nombre\npremier sup\u00e9rieur \u00e0 10, vous v\u00e9rifiez chaque nombre (&gt;10) jusqu&rsquo;\u00e0 ce que\nvous trouviez un nombre premier, ici 11.<\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<h2><span class=\"ez-toc-section\" id=\"2_Presenter_les_resultats_fractionnaires_sous_forme_irreductible\"><\/span>2. Pr\u00e9senter les r\u00e9sultats fractionnaires sous forme irr\u00e9ductible :<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\">Une fraction est dite irr\u00e9ductible si le num\u00e9rateur et le\nd\u00e9nominateur sont premiers entre eux, c&rsquo;est-\u00e0-dire qu&rsquo;ils n&rsquo;ont pas d&rsquo;autres\ndiviseurs communs que 1.<\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\"><b>\u00c9tapes pour simplifier une fraction :<\/b><\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\">1. <b>Trouver le PGCD (Plus Grand Commun Diviseur)<\/b> :\nD\u00e9terminez le plus grand nombre qui peut diviser \u00e0 la fois le num\u00e9rateur et le\nd\u00e9nominateur de la fraction.<\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\">2. <b>Diviser<\/b> : Divisez \u00e0 la fois le num\u00e9rateur et le\nd\u00e9nominateur par le PGCD trouv\u00e9.<\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\">3. <b>\u00c9crire la fraction simplifi\u00e9e<\/b> : La fraction\nobtenue apr\u00e8s division est la fraction irr\u00e9ductible.<\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\"><b>Exemple<\/b> : Pour simplifier la fraction\n<span class=\"katex-eq\" data-katex-display=\"false\">20\/45<\/span>:<\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\">&#8211; PGCD(20, 45) = 5<\/p>\n\n<p class=\"MsoNormal\">&#8211; Fraction irr\u00e9ductible = <span class=\"katex-eq\" data-katex-display=\"false\">20 \u00f7 5<\/span>\/<span class=\"katex-eq\" data-katex-display=\"false\">45 \u00f7\n5<\/span> = <span class=\"katex-eq\" data-katex-display=\"false\">4\/9<\/span><\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\">Ainsi, <span class=\"katex-eq\" data-katex-display=\"false\">20\/45<\/span> peut \u00eatre pr\u00e9sent\u00e9 sous forme\nirr\u00e9ductible comme <span class=\"katex-eq\" data-katex-display=\"false\">4\/9<\/span>.<\/p>\n\n\n\n\n\n<style>@font-face\n\t{font-family:\"Cambria Math\";\n\tpanose-1:2 4 5 3 5 4 6 3 2 4;\n\tmso-font-charset:0;\n\tmso-generic-font-family:roman;\n\tmso-font-pitch:variable;\n\tmso-font-signature:-536870145 1107305727 0 0 415 0;}@font-face\n\t{font-family:Calibri;\n\tpanose-1:2 15 5 2 2 2 4 3 2 4;\n\tmso-font-charset:0;\n\tmso-generic-font-family:swiss;\n\tmso-font-pitch:variable;\n\tmso-font-signature:-536859905 -1073732485 9 0 511 0;}@font-face\n\t{font-family:\"Calibri Light\";\n\tpanose-1:2 15 3 2 2 2 4 3 2 4;\n\tmso-font-charset:0;\n\tmso-generic-font-family:swiss;\n\tmso-font-pitch:variable;\n\tmso-font-signature:-469750017 -1073732485 9 0 511 0;}p.MsoNormal, li.MsoNormal, 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data-id=\"789777a\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-dd93843\" data-id=\"dd93843\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-b1d0d5c elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"b1d0d5c\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-7e963bc\" data-id=\"7e963bc\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-40909d1 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"40909d1\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-3a01f62\" data-id=\"3a01f62\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Utiliser les notions de multiple, diviseur et de nombre premier Introduction &nbsp; La compr\u00e9hension des notions de multiple et de diviseur est fondamentale en math\u00e9matiques. Ces concepts nous permettent de classer et de manipuler les nombres de diff\u00e9rentes mani\u00e8res, facilitant ainsi la r\u00e9solution de probl\u00e8mes plus complexes. Les nombres pairs et impairs sont des cas [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"elementor_canvas","format":"standard","meta":{"footnotes":""},"categories":[25,26,5],"tags":[],"_links":{"self":[{"href":"https:\/\/www.maxdecours.com\/maxblog\/wp-json\/wp\/v2\/posts\/1888"}],"collection":[{"href":"https:\/\/www.maxdecours.com\/maxblog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.maxdecours.com\/maxblog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.maxdecours.com\/maxblog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.maxdecours.com\/maxblog\/wp-json\/wp\/v2\/comments?post=1888"}],"version-history":[{"count":20,"href":"https:\/\/www.maxdecours.com\/maxblog\/wp-json\/wp\/v2\/posts\/1888\/revisions"}],"predecessor-version":[{"id":2030,"href":"https:\/\/www.maxdecours.com\/maxblog\/wp-json\/wp\/v2\/posts\/1888\/revisions\/2030"}],"wp:attachment":[{"href":"https:\/\/www.maxdecours.com\/maxblog\/wp-json\/wp\/v2\/media?parent=1888"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.maxdecours.com\/maxblog\/wp-json\/wp\/v2\/categories?post=1888"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.maxdecours.com\/maxblog\/wp-json\/wp\/v2\/tags?post=1888"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}