{"id":226338,"date":"2025-06-05T06:14:52","date_gmt":"2025-06-05T06:14:52","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=226338"},"modified":"2025-06-05T06:14:55","modified_gmt":"2025-06-05T06:14:55","slug":"what-is-the-gcf-of-72-and-50","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/05\/what-is-the-gcf-of-72-and-50\/","title":{"rendered":"What is the GCF of 72 and 50"},"content":{"rendered":"\n

What is the GCF of 72 and 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 72 and 50 is 2<\/strong>.<\/h3>\n\n\n\n
\n\n\n\n

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

The Greatest Common Factor (GCF)<\/strong> of two numbers is the largest number that divides both of them exactly, without leaving a remainder. To find the GCF of 72 and 50, we can use two methods: listing the factors<\/strong> and prime factorization<\/strong>.<\/p>\n\n\n\n

\n\n\n\n

Method 1: Listing the Factors<\/strong><\/h4>\n\n\n\n
    \n
  1. Factors of 72<\/strong>:
    The numbers that divide 72 exactly are:
    1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72<\/li>\n\n\n\n
  2. Factors of 50<\/strong>:
    The numbers that divide 50 exactly are:
    1, 2, 5, 10, 25, 50<\/li>\n\n\n\n
  3. Common Factors<\/strong>:
    From the lists above, the common factors of 72 and 50 are:
    1 and 2<\/strong><\/li>\n\n\n\n
  4. Greatest Common Factor<\/strong>:
    The largest number common to both lists is 2<\/strong>.<\/li>\n<\/ol>\n\n\n\n
    \n\n\n\n

    Method 2: Prime Factorization<\/strong><\/h4>\n\n\n\n
      \n
    1. Prime Factorization of 72<\/strong>:
      72 = 2 \u00d7 2 \u00d7 2 \u00d7 3 \u00d7 3 = 2\u00b3 \u00d7 3\u00b2<\/strong><\/li>\n\n\n\n
    2. Prime Factorization of 50<\/strong>:
      50 = 2 \u00d7 5 \u00d7 5 = 2 \u00d7 5\u00b2<\/strong><\/li>\n\n\n\n
    3. Common Prime Factors<\/strong>:
      The only common prime factor is 2<\/strong>, and it appears to the power of 1 in both factorizations.<\/li>\n\n\n\n
    4. GCF<\/strong>:
      Multiply the lowest power of each common prime factor:
      GCF = 2\u00b9<\/strong> = 2<\/strong><\/li>\n<\/ol>\n\n\n\n
      \n\n\n\n

      Conclusion<\/strong>:<\/h4>\n\n\n\n

      The GCF of 72 and 50 is 2<\/strong>, meaning that 2 is the largest number that evenly divides both. This is important in real-life problems like simplifying fractions or determining shared cycles in timing or scheduling. Understanding GCF helps build a foundation for more complex math, such as finding least common multiples (LCM), simplifying ratios, and solving problems involving division and grouping.<\/p>\n\n\n\n

      \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

      What is the GCF of 72 and 50 The Correct Answer and Explanation is: The Greatest Common Factor (GCF) of 72 and 50 is 2. Explanation The Greatest Common Factor (GCF) of two numbers is the largest number that divides both of them exactly, without leaving a remainder. To find the GCF of 72 and […]<\/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-226338","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/226338","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=226338"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/226338\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=226338"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=226338"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=226338"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}