{"id":264565,"date":"2025-07-21T14:00:42","date_gmt":"2025-07-21T14:00:42","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=264565"},"modified":"2025-07-21T14:00:45","modified_gmt":"2025-07-21T14:00:45","slug":"what-is-the-greatest-common-factor-of-42-126-and-210","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/21\/what-is-the-greatest-common-factor-of-42-126-and-210\/","title":{"rendered":"What is the greatest common factor of 42, 126, and 210"},"content":{"rendered":"\n

What is the greatest common factor of 42, 126, and 210 ?<\/p>\n\n\n\n

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

To find the greatest common factor (GCF) of 42, 126, and 210, we begin by determining the prime factorization of each number.<\/p>\n\n\n\n

    \n
  1. Prime factorization of 42:<\/strong>\n
      \n
    • Start with the smallest prime number, 2.<\/li>\n\n\n\n
    • 42 \u00f7 2 = 21.<\/li>\n\n\n\n
    • Now factor 21: 21 \u00f7 3 = 7.<\/li>\n\n\n\n
    • Since 7 is prime, the prime factorization of 42 is: 2\u00d73\u00d772 \\times 3 \\times 7.<\/li>\n<\/ul>\n<\/li>\n\n\n\n
    • Prime factorization of 126:<\/strong>\n
        \n
      • 126 \u00f7 2 = 63.<\/li>\n\n\n\n
      • Factor 63: 63 \u00f7 3 = 21.<\/li>\n\n\n\n
      • Factor 21: 21 \u00f7 3 = 7.<\/li>\n\n\n\n
      • So, the prime factorization of 126 is: 2\u00d732\u00d772 \\times 3^2 \\times 7.<\/li>\n<\/ul>\n<\/li>\n\n\n\n
      • Prime factorization of 210:<\/strong>\n
          \n
        • 210 \u00f7 2 = 105.<\/li>\n\n\n\n
        • Factor 105: 105 \u00f7 3 = 35.<\/li>\n\n\n\n
        • Factor 35: 35 \u00f7 5 = 7.<\/li>\n\n\n\n
        • So, the prime factorization of 210 is: 2\u00d73\u00d75\u00d772 \\times 3 \\times 5 \\times 7.<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n

          Now that we have the prime factorizations, we find the common factors between all three numbers. The prime factors they share are:<\/p>\n\n\n\n

            \n
          • 2<\/li>\n\n\n\n
          • 3<\/li>\n\n\n\n
          • 7<\/li>\n<\/ul>\n\n\n\n

            The greatest common factor is the product of these common prime factors:
            2\u00d73\u00d77=422 \\times 3 \\times 7 = 42.<\/p>\n\n\n\n

            Therefore, the greatest common factor (GCF) of 42, 126, and 210 is 42<\/strong>.<\/p>\n\n\n\n

            To verify, we divide each of the original numbers by 42:<\/p>\n\n\n\n

              \n
            • 42 \u00f7 42 = 1<\/li>\n\n\n\n
            • 126 \u00f7 42 = 3<\/li>\n\n\n\n
            • 210 \u00f7 42 = 5<\/li>\n<\/ul>\n\n\n\n

              Since all results are integers, the GCF is confirmed to be 42.<\/p>\n","protected":false},"excerpt":{"rendered":"

              What is the greatest common factor of 42, 126, and 210 ? The correct answer and explanation is: To find the greatest common factor (GCF) of 42, 126, and 210, we begin by determining the prime factorization of each number. Now that we have the prime factorizations, we find the common factors between all three […]<\/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-264565","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/264565","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=264565"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/264565\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=264565"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=264565"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=264565"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}