{"id":227955,"date":"2025-06-06T16:13:41","date_gmt":"2025-06-06T16:13:41","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=227955"},"modified":"2025-06-06T16:13:43","modified_gmt":"2025-06-06T16:13:43","slug":"find-the-gcf-of-96x5-and-64x2","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/06\/find-the-gcf-of-96x5-and-64x2\/","title":{"rendered":"Find the GCF of 96×5 and 64×2"},"content":{"rendered":"\n

Find the GCF of 96×5 and 64×2<\/p>\n\n\n\n

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

\u2705 Greatest Common Factor (GCF) of 96x\u2075 and 64x\u00b2:<\/strong><\/h3>\n\n\n\n

Answer:<\/strong>
The GCF of 96x\u2075<\/strong> and 64x\u00b2<\/strong> is 32x\u00b2<\/strong>.<\/p>\n\n\n\n

\n\n\n\n

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

To find the Greatest Common Factor (GCF)<\/strong> of two algebraic expressions, we must find the largest expression that divides both terms exactly\u2014this includes both their numerical coefficients<\/strong> and their variable parts<\/strong>.<\/p>\n\n\n\n

Let\u2019s break it down step by step.<\/p>\n\n\n\n

\n\n\n\n

1. Find the GCF of the numerical coefficients:<\/strong><\/h4>\n\n\n\n

The two coefficients are:<\/p>\n\n\n\n

    \n
  • 96<\/strong><\/li>\n\n\n\n
  • 64<\/strong><\/li>\n<\/ul>\n\n\n\n

    We factor each number:<\/p>\n\n\n\n

      \n
    • 96 = 2\u2075 \u00d7 3<\/li>\n\n\n\n
    • 64 = 2\u2076<\/li>\n<\/ul>\n\n\n\n

      The common factor is the lowest power of the common prime factor<\/strong>, which is 2:<\/p>\n\n\n\n

        \n
      • GCF(96, 64) = 2\u2075 = 32<\/strong><\/li>\n<\/ul>\n\n\n\n
        \n\n\n\n

        2. Find the GCF of the variable parts:<\/strong><\/h4>\n\n\n\n

        We have:<\/p>\n\n\n\n

          \n
        • x\u2075<\/li>\n\n\n\n
        • x\u00b2<\/li>\n<\/ul>\n\n\n\n

          When variables are raised to powers, the GCF is the variable raised to the smallest exponent<\/strong>:<\/p>\n\n\n\n

            \n
          • GCF(x\u2075, x\u00b2) = x\u00b2<\/li>\n<\/ul>\n\n\n\n
            \n\n\n\n

            3. Combine the two GCFs:<\/strong><\/h4>\n\n\n\n

            Now combine the GCF of the numerical coefficients (32) and the variable part (x\u00b2):<\/p>\n\n\n\n

              \n
            • GCF(96x\u2075, 64x\u00b2) = 32x\u00b2<\/strong><\/li>\n<\/ul>\n\n\n\n
              \n\n\n\n

              \ud83d\udd01 Verification:<\/strong><\/h3>\n\n\n\n

              Let\u2019s divide both expressions by 32x\u00b2:<\/p>\n\n\n\n

                \n
              • 96x\u2075 \u00f7 32x\u00b2 = 3x\u00b3<\/li>\n\n\n\n
              • 64x\u00b2 \u00f7 32x\u00b2 = 2<\/li>\n<\/ul>\n\n\n\n

                Both divisions give whole expressions, confirming that 32x\u00b2<\/strong> is indeed a common factor<\/strong>.<\/p>\n\n\n\n

                Also, it is the greatest<\/strong> common factor because no larger number or variable expression can divide both 96x\u2075 and 64x\u00b2 without leaving a remainder.<\/p>\n\n\n\n

                \n\n\n\n

                \u2705 Final Answer: 32x\u00b2<\/strong><\/h3>\n\n\n\n
                \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

                Find the GCF of 96×5 and 64×2 The Correct Answer and Explanation is: \u2705 Greatest Common Factor (GCF) of 96x\u2075 and 64x\u00b2: Answer:The GCF of 96x\u2075 and 64x\u00b2 is 32x\u00b2. Explanation: To find the Greatest Common Factor (GCF) of two algebraic expressions, we must find the largest expression that divides both terms exactly\u2014this includes both […]<\/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-227955","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/227955","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=227955"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/227955\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=227955"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=227955"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=227955"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}