{"id":266954,"date":"2025-07-23T08:23:34","date_gmt":"2025-07-23T08:23:34","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=266954"},"modified":"2025-07-23T08:23:36","modified_gmt":"2025-07-23T08:23:36","slug":"find-the-gcf-of-the-following-set-of-numbers-260-80-50","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/23\/find-the-gcf-of-the-following-set-of-numbers-260-80-50\/","title":{"rendered":"Find the GCF of the following set of numbers 260, 80, 50"},"content":{"rendered":"\n

Find the GCF of the following set of numbers 260, 80, 50<\/p>\n\n\n\n

The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n

The greatest common factor (GCF) of 260, 80, and 50 is 10<\/strong>.<\/p>\n\n\n\n

Explanation:<\/h3>\n\n\n\n

To find the GCF, also known as the greatest common divisor (GCD), follow these steps:<\/p>\n\n\n\n

    \n
  1. Find the prime factorization of each number:<\/strong>\n
      \n
    • 260<\/strong>: Divide by 2 (the smallest prime number):
      260 \u00f7 2 = 130
      130 \u00f7 2 = 65
      65 \u00f7 5 = 13 (which is prime)
      Therefore, the prime factorization of 260 is: 260=22\u00d75\u00d713260 = 2^2 \\times 5 \\times 13<\/li>\n\n\n\n
    • 80<\/strong>: Divide by 2:
      80 \u00f7 2 = 40
      40 \u00f7 2 = 20
      20 \u00f7 2 = 10
      10 \u00f7 2 = 5 (which is prime)
      Therefore, the prime factorization of 80 is: 80=24\u00d7580 = 2^4 \\times 5<\/li>\n\n\n\n
    • 50<\/strong>: Divide by 2 and 5:
      50 \u00f7 2 = 25
      25 \u00f7 5 = 5
      Therefore, the prime factorization of 50 is: 50=2\u00d75250 = 2 \\times 5^2<\/li>\n<\/ul>\n<\/li>\n\n\n\n
    • Identify the common prime factors<\/strong>:
      From the prime factorizations, the common prime factors are 2 and 5.<\/li>\n\n\n\n
    • Choose the smallest power of each common prime factor<\/strong>:\n
        \n
      • For 2, the smallest power is 212^1 (since 260 has 222^2, 80 has 242^4, and 50 has 212^1).<\/li>\n\n\n\n
      • For 5, the smallest power is 515^1 (since all three numbers contain 515^1 or higher powers).<\/li>\n<\/ul>\n<\/li>\n\n\n\n
      • Multiply the smallest powers of the common factors<\/strong>: GCF=21\u00d751=2\u00d75=10GCF = 2^1 \\times 5^1 = 2 \\times 5 = 10<\/li>\n<\/ol>\n\n\n\n

        Thus, the GCF of 260, 80, and 50 is 10<\/strong>. This is the largest number that divides all three numbers without leaving a remainder.<\/p>\n","protected":false},"excerpt":{"rendered":"

        Find the GCF of the following set of numbers 260, 80, 50 The correct answer and explanation is: The greatest common factor (GCF) of 260, 80, and 50 is 10. Explanation: To find the GCF, also known as the greatest common divisor (GCD), follow these steps: Thus, the GCF of 260, 80, and 50 is […]<\/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-266954","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/266954","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=266954"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/266954\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=266954"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=266954"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=266954"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}