{"id":225195,"date":"2025-06-04T05:01:08","date_gmt":"2025-06-04T05:01:08","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=225195"},"modified":"2025-06-04T05:01:11","modified_gmt":"2025-06-04T05:01:11","slug":"what-is-the-greatest-common-factor-of-540-and-600","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/04\/what-is-the-greatest-common-factor-of-540-and-600\/","title":{"rendered":"what is the greatest common factor of 540 and 600"},"content":{"rendered":"\n

what is the greatest common factor of 540 and 600
what is the greatest common factor of 540 and 600<\/p>\n\n\n\n

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

The greatest common factor (GCF)<\/strong> of 540 and 600<\/strong> is 60<\/strong>.<\/p>\n\n\n\n

\n\n\n\n

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

To understand why 60<\/strong> is the greatest common factor (GCF) of 540 and 600, we must first understand what a GCF is. The GCF of two numbers is the largest number that divides both numbers without leaving a remainder.<\/p>\n\n\n\n

There are a few ways to find the GCF, but the most common is by prime factorization<\/strong>.<\/p>\n\n\n\n

\n\n\n\n

Step 1: Prime factorization<\/h3>\n\n\n\n

540<\/strong>
First, divide by 2 (the smallest prime number):<\/p>\n\n\n\n

    \n
  • 540 \u00f7 2 = 270<\/li>\n\n\n\n
  • 270 \u00f7 2 = 135
    Next, divide 135 by 3:<\/li>\n\n\n\n
  • 135 \u00f7 3 = 45<\/li>\n\n\n\n
  • 45 \u00f7 3 = 15<\/li>\n\n\n\n
  • 15 \u00f7 3 = 5
    Now 5 is a prime number.<\/li>\n<\/ul>\n\n\n\n

    So,
    540 = 2\u00b2 \u00d7 3\u00b3 \u00d7 5<\/strong><\/p>\n\n\n\n

    \n\n\n\n

    600<\/strong><\/p>\n\n\n\n

      \n
    • 600 \u00f7 2 = 300<\/li>\n\n\n\n
    • 300 \u00f7 2 = 150<\/li>\n\n\n\n
    • 150 \u00f7 2 = 75
      Now divide by 3:<\/li>\n\n\n\n
    • 75 \u00f7 3 = 25
      Then divide 25 by 5:<\/li>\n\n\n\n
    • 25 \u00f7 5 = 5<\/li>\n\n\n\n
    • 5 \u00f7 5 = 1<\/li>\n<\/ul>\n\n\n\n

      So,
      600 = 2\u00b3 \u00d7 3 \u00d7 5\u00b2<\/strong><\/p>\n\n\n\n

      \n\n\n\n

      Step 2: Identify common prime factors<\/h3>\n\n\n\n

      Now compare the prime factorizations:<\/p>\n\n\n\n

        \n
      • 540 = 2\u00b2 \u00d7 3\u00b3 \u00d7 5<\/strong><\/li>\n\n\n\n
      • 600 = 2\u00b3 \u00d7 3 \u00d7 5\u00b2<\/strong><\/li>\n<\/ul>\n\n\n\n

        Take the lowest powers<\/strong> of each common prime factor:<\/p>\n\n\n\n

          \n
        • 2: min(2, 3) = 2 \u2192 2\u00b2<\/li>\n\n\n\n
        • 3: min(3, 1) = 1 \u2192 3\u00b9<\/li>\n\n\n\n
        • 5: min(1, 2) = 1 \u2192 5\u00b9<\/li>\n<\/ul>\n\n\n\n

          Multiply these together:
          GCF = 2\u00b2 \u00d7 3 \u00d7 5 = 4 \u00d7 3 \u00d7 5 = 60<\/strong><\/p>\n\n\n\n

          \n\n\n\n

          Final Answer:<\/h3>\n\n\n\n

          \u2705 The greatest common factor of 540 and 600 is 60.<\/strong><\/p>\n\n\n\n

          This method ensures we accurately determine the highest number that divides both integers completely<\/p>\n\n\n\n

          \"\"<\/figure>\n\n\n\n

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

          what is the greatest common factor of 540 and 600what is the greatest common factor of 540 and 600 The Correct Answer and Explanation is: The greatest common factor (GCF) of 540 and 600 is 60. Explanation To understand why 60 is the greatest common factor (GCF) of 540 and 600, we must first understand […]<\/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-225195","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/225195","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=225195"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/225195\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=225195"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=225195"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=225195"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}