{"id":263728,"date":"2025-07-21T08:38:07","date_gmt":"2025-07-21T08:38:07","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=263728"},"modified":"2025-07-21T08:38:09","modified_gmt":"2025-07-21T08:38:09","slug":"what-is-the-greatest-common-factor-of-24-and-64","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/21\/what-is-the-greatest-common-factor-of-24-and-64\/","title":{"rendered":"What is the greatest common factor of 24 and 64"},"content":{"rendered":"\n<p>What is the greatest common factor of 24 and 64? a. 8 b. 4 c. 12 d. 36<\/p>\n\n\n\n<p><strong>The Correct Answer and Explanation is:<\/strong><\/p>\n\n\n\n<p>The greatest common factor (GCF) of 24 and 64 is <strong>a. 8<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>To find the greatest common factor, we need to first determine the prime factorizations of both numbers and then identify the highest number that divides both.<\/p>\n\n\n\n<p><strong>1. Prime factorization of 24:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>24 can be divided by 2 (the smallest prime number):<br>24 \u00f7 2 = 12<br>12 \u00f7 2 = 6<br>6 \u00f7 2 = 3<br>3 \u00f7 3 = 1<br>So, the prime factorization of 24 is:<br><strong>2 \u00d7 2 \u00d7 2 \u00d7 3<\/strong> or <strong>2\u00b3 \u00d7 3<\/strong>.<\/li>\n<\/ul>\n\n\n\n<p><strong>2. Prime factorization of 64:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>64 is also divisible by 2:<br>64 \u00f7 2 = 32<br>32 \u00f7 2 = 16<br>16 \u00f7 2 = 8<br>8 \u00f7 2 = 4<br>4 \u00f7 2 = 2<br>2 \u00f7 2 = 1<br>So, the prime factorization of 64 is:<br><strong>2 \u00d7 2 \u00d7 2 \u00d7 2 \u00d7 2 \u00d7 2<\/strong> or <strong>2\u2076<\/strong>.<\/li>\n<\/ul>\n\n\n\n<p><strong>3. Identify the common factors:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The prime factorizations are:<br>24 = <strong>2\u00b3 \u00d7 3<\/strong><br>64 = <strong>2\u2076<\/strong><\/li>\n\n\n\n<li>The common factor between 24 and 64 is <strong>2\u00b3<\/strong> (since both numbers have at least three factors of 2).<\/li>\n<\/ul>\n\n\n\n<p><strong>4. Find the greatest common factor:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The greatest common factor is the highest power of the common prime factor, which in this case is <strong>2\u00b3<\/strong> = <strong>8<\/strong>.<\/li>\n<\/ul>\n\n\n\n<p>Thus, the greatest common factor of 24 and 64 is <strong>8<\/strong>, and the correct answer is <strong>a. 8<\/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-banner6-1323.jpeg\" alt=\"\" class=\"wp-image-263735\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>What is the greatest common factor of 24 and 64? a. 8 b. 4 c. 12 d. 36 The Correct Answer and Explanation is: The greatest common factor (GCF) of 24 and 64 is a. 8. Explanation: To find the greatest common factor, we need to first determine the prime factorizations of both numbers and [&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-263728","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/263728","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=263728"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/263728\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=263728"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=263728"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=263728"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}