{"id":266956,"date":"2025-07-23T08:24:55","date_gmt":"2025-07-23T08:24:55","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=266956"},"modified":"2025-07-23T08:24:57","modified_gmt":"2025-07-23T08:24:57","slug":"what-is-the-greatest-common-factor-gcf-of-80-and-50","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/23\/what-is-the-greatest-common-factor-gcf-of-80-and-50\/","title":{"rendered":"What is the greatest common factor (GCF) of 80 and 50"},"content":{"rendered":"\n<p>What is the greatest common factor (GCF) of 80 and 50?<\/p>\n\n\n\n<p> A. 25 <\/p>\n\n\n\n<p>B. 10 <\/p>\n\n\n\n<p>C. 5 <\/p>\n\n\n\n<p>D. 400<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\">The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>The correct answer is <strong>B. 10<\/strong>.<\/p>\n\n\n\n<p>To find the greatest common factor (GCF) of 80 and 50, we need to identify the largest number that divides both 80 and 50 evenly.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Find the prime factorization of each number<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>80<\/strong> can be factored as follows:\n<ul class=\"wp-block-list\">\n<li>80 \u00f7 2 = 40<\/li>\n\n\n\n<li>40 \u00f7 2 = 20<\/li>\n\n\n\n<li>20 \u00f7 2 = 10<\/li>\n\n\n\n<li>10 \u00f7 2 = 5<\/li>\n\n\n\n<li>5 \u00f7 5 = 1<\/li>\n\n\n\n<li>Therefore, the prime factorization of 80 is 24\u00d752^4 \\times 5.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>50<\/strong> can be factored as follows:\n<ul class=\"wp-block-list\">\n<li>50 \u00f7 2 = 25<\/li>\n\n\n\n<li>25 \u00f7 5 = 5<\/li>\n\n\n\n<li>5 \u00f7 5 = 1<\/li>\n\n\n\n<li>Therefore, the prime factorization of 50 is 2\u00d7522 \\times 5^2.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Identify the common factors<\/h3>\n\n\n\n<p>From the prime factorizations:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The prime factors of 80 are 24\u00d752^4 \\times 5.<\/li>\n\n\n\n<li>The prime factors of 50 are 2\u00d7522 \\times 5^2.<\/li>\n<\/ul>\n\n\n\n<p>The common factors between 80 and 50 are <strong>2<\/strong> and <strong>5<\/strong>. We take the smallest power of each common prime factor:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>For 22, the smallest power is 212^1.<\/li>\n\n\n\n<li>For 55, the smallest power is 515^1.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Multiply the common factors<\/h3>\n\n\n\n<p>The greatest common factor is the product of these common factors:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>21\u00d751=2\u00d75=102^1 \\times 5^1 = 2 \\times 5 = 10.<\/li>\n<\/ul>\n\n\n\n<p>Thus, the greatest common factor of 80 and 50 is <strong>10<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Conclusion:<\/h3>\n\n\n\n<p>The greatest common factor of 80 and 50 is <strong>10<\/strong>, which is option B. The GCF is the largest number that can evenly divide both numbers, and through prime factorization, we have determined that 10 is the highest such number.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>What is the greatest common factor (GCF) of 80 and 50? A. 25 B. 10 C. 5 D. 400 The correct answer and explanation is: The correct answer is B. 10. To find the greatest common factor (GCF) of 80 and 50, we need to identify the largest number that divides both 80 and 50 [&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-266956","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/266956","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=266956"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/266956\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=266956"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=266956"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=266956"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}