{"id":264255,"date":"2025-07-21T12:01:21","date_gmt":"2025-07-21T12:01:21","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=264255"},"modified":"2025-07-21T12:01:22","modified_gmt":"2025-07-21T12:01:22","slug":"what-is-the-common-factor-of-9-and-12","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/21\/what-is-the-common-factor-of-9-and-12\/","title":{"rendered":"What is the common factor of 9 and 12"},"content":{"rendered":"\n<p>What is the common factor of 9 and 12<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-0-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>The common factors of 9 and 12 are the numbers that divide both 9 and 12 without leaving a remainder. To find the common factors, we need to first determine the factors of each number.<\/p>\n\n\n\n<p><strong>Factors of 9<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The factors of 9 are 1, 3, and 9 because 9 can be divided evenly by these numbers.<\/li>\n<\/ul>\n\n\n\n<p><strong>Factors of 12<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The factors of 12 are 1, 2, 3, 4, 6, and 12 because 12 can be divided evenly by these numbers.<\/li>\n<\/ul>\n\n\n\n<p>Next, we look for the numbers that appear in both lists of factors. These common numbers are:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>1 and 3<\/li>\n<\/ul>\n\n\n\n<p>Therefore, the common factors of 9 and 12 are <strong>1<\/strong> and <strong>3<\/strong>. The <strong>greatest common factor (GCF)<\/strong>, also known as the <strong>greatest common divisor (GCD)<\/strong>, is the largest number that appears in both lists, which is <strong>3<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>To better understand why 3 is the greatest common factor, we can consider the process of finding the greatest common divisor (GCD) using prime factorization:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Prime factorization of 9<\/strong>:\n<ul class=\"wp-block-list\">\n<li>9 is divisible by 3, and 3 is a prime number.<\/li>\n\n\n\n<li>So, the prime factorization of 9 is 9=329 = 3^29=32.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Prime factorization of 12<\/strong>:\n<ul class=\"wp-block-list\">\n<li>12 is divisible by 2 and 3. When you divide 12 by 2, you get 6, and dividing 6 by 3 gives you 2.<\/li>\n\n\n\n<li>So, the prime factorization of 12 is 12=22\u00d7312 = 2^2 \\times 312=22\u00d73.<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n<p>Now, when we compare the prime factorizations of 9 and 12, the only common prime factor is 3, and the smallest power of 3 that appears in both is 313^131, which gives the GCD as <strong>3<\/strong>.<\/p>\n\n\n\n<p>Thus, the greatest common factor of 9 and 12 is <strong>3<\/strong>.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner6-1383.jpeg\" alt=\"\" class=\"wp-image-264266\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>What is the common factor of 9 and 12 The Correct Answer and Explanation is: The common factors of 9 and 12 are the numbers that divide both 9 and 12 without leaving a remainder. To find the common factors, we need to first determine the factors of each number. Factors of 9: Factors of [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-264255","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/264255","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=264255"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/264255\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=264255"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=264255"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=264255"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}