{"id":237301,"date":"2025-06-17T06:32:14","date_gmt":"2025-06-17T06:32:14","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=237301"},"modified":"2025-06-17T06:32:16","modified_gmt":"2025-06-17T06:32:16","slug":"what-is-the-gcf-of-125-100-and-125-with-a-solution","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/17\/what-is-the-gcf-of-125-100-and-125-with-a-solution\/","title":{"rendered":"what is the gcf of 125 100 and 125 with a solution"},"content":{"rendered":"\n

what is the gcf of 125 100 and 125 with a solution<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

Correct Answer:<\/strong>
The greatest common factor (GCF) of 125<\/strong>, 100<\/strong>, and 125<\/strong> is 25<\/strong>.<\/p>\n\n\n\n

\n\n\n\n

Solution:<\/strong><\/h3>\n\n\n\n

We are asked to find the greatest common factor (GCF) of 125<\/strong>, 100<\/strong>, and 125<\/strong>.<\/p>\n\n\n\n

Step 1: Find the prime factorization of each number<\/strong><\/h4>\n\n\n\n
    \n
  • 125<\/strong>
    125 is divisible by 5:
    125 \u00f7 5 = 25
    25 \u00f7 5 = 5
    5 \u00f7 5 = 1
    So, 125 = 5 \u00d7 5 \u00d7 5 = 5\u00b3<\/strong><\/li>\n\n\n\n
  • 100<\/strong>
    100 \u00f7 2 = 50
    50 \u00f7 2 = 25
    25 \u00f7 5 = 5
    5 \u00f7 5 = 1
    So, 100 = 2\u00b2 \u00d7 5\u00b2<\/li>\n<\/ul>\n\n\n\n

    Step 2: Identify common prime factors<\/strong><\/h4>\n\n\n\n

    We compare the prime factors of:<\/p>\n\n\n\n

      \n
    • 125 = 5\u00b3<\/li>\n\n\n\n
    • 100 = 2\u00b2 \u00d7 5\u00b2<\/li>\n<\/ul>\n\n\n\n

      The only common prime factor is 5<\/strong>, and we take the lowest power<\/strong> of this factor among the numbers.<\/p>\n\n\n\n

        \n
      • 5 appears as 5\u00b3 in 125 and 5\u00b2 in 100<\/li>\n\n\n\n
      • The smallest power is 5\u00b2 = 25<\/strong><\/li>\n<\/ul>\n\n\n\n

        So, GCF = 25<\/strong><\/p>\n\n\n\n

        We can ignore the repeated 125, since the GCF of 125, 100, and 125 is the same as the GCF of just 125 and 100.<\/p>\n\n\n\n

        \n\n\n\n

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

        The greatest common factor (GCF) of a set of numbers is the largest number that can divide all the given numbers exactly, without leaving a remainder. This is especially useful when simplifying fractions, factoring polynomials, or solving word problems involving groups.<\/p>\n\n\n\n

        To find the GCF of 125, 100, and 125, we start by performing a prime factorization<\/strong> of each number. Prime factorization breaks down a number into its building blocks\u2014its prime numbers. For 125, the prime factor is 5. Dividing repeatedly by 5 gives 125 = 5 \u00d7 5 \u00d7 5 or 5\u00b3. For 100, dividing by its smallest prime factors, we get 100 = 2 \u00d7 2 \u00d7 5 \u00d7 5 or 2\u00b2 \u00d7 5\u00b2.<\/p>\n\n\n\n

        Next, we identify the common prime factors shared by all numbers. Both 125 and 100 share the prime factor 5. While 125 has 5\u00b3 and 100 has 5\u00b2, we select the lowest power<\/strong> of the common factor, which is 5\u00b2 = 25. This is because a higher power would not divide evenly into the number with the smaller power.<\/p>\n\n\n\n

        The number 25 can divide both 125 and 100 exactly, and since it is the largest such number, it is the GCF.<\/p>\n\n\n\n

        Therefore, the greatest common factor of 125, 100, and 125 is 25<\/strong>.<\/p>\n\n\n\n

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

        what is the gcf of 125 100 and 125 with a solution The Correct Answer and Explanation is: Correct Answer:The greatest common factor (GCF) of 125, 100, and 125 is 25. Solution: We are asked to find the greatest common factor (GCF) of 125, 100, and 125. Step 1: Find the prime factorization of each […]<\/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-237301","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/237301","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=237301"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/237301\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=237301"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=237301"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=237301"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}