{"id":253420,"date":"2025-07-12T05:03:57","date_gmt":"2025-07-12T05:03:57","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=253420"},"modified":"2025-07-12T05:03:59","modified_gmt":"2025-07-12T05:03:59","slug":"write-32-24-as-a-product-of-two-factors-using-the-gcf-and-the-distributive-property","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/12\/write-32-24-as-a-product-of-two-factors-using-the-gcf-and-the-distributive-property\/","title":{"rendered":"Write 32 +24 as a product of two factors using the gcf and the distributive property"},"content":{"rendered":"\n<p>Write 32 +24 as a product of two factors using the gcf and the distributive property<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\">The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To express 32+2432 + 24 as a product of two factors using the greatest common factor (GCF) and the distributive property, we begin by identifying the GCF of 32 and 24.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Find the GCF of 32 and 24<\/h3>\n\n\n\n<p>The GCF is the largest number that divides both 32 and 24 without leaving a remainder. To find it, list the factors of each number:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Factors of 32: 1, 2, 4, 8, 16, 32<\/li>\n\n\n\n<li>Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24<\/li>\n<\/ul>\n\n\n\n<p>The greatest common factor is <strong>8<\/strong>, since 8 is the largest number that appears in both lists.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Factor out the GCF<\/h3>\n\n\n\n<p>Now that we know the GCF is 8, we can factor both 32 and 24 by dividing each number by 8: 32=8\u00d7432 = 8 \\times 4 24=8\u00d7324 = 8 \\times 3<\/p>\n\n\n\n<p>Thus, we can rewrite the original expression 32+2432 + 24 as: 32+24=(8\u00d74)+(8\u00d73)32 + 24 = (8 \\times 4) + (8 \\times 3)<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Apply the distributive property<\/h3>\n\n\n\n<p>The distributive property states that a(b+c)=ab+aca(b + c) = ab + ac. In this case, we can factor out the 8: 32+24=8\u00d7(4+3)32 + 24 = 8 \\times (4 + 3)<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 4: Simplify the expression<\/h3>\n\n\n\n<p>Now, simplify inside the parentheses: 4+3=74 + 3 = 7<\/p>\n\n\n\n<p>Thus, the expression becomes: 32+24=8\u00d7732 + 24 = 8 \\times 7<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Conclusion<\/h3>\n\n\n\n<p>The sum of 32 and 24 can be written as the product of two factors, 8\u00d778 \\times 7. This is the factorization using the GCF and the distributive property. The distributive property allows us to rewrite the sum as a multiplication, which can be useful in simplifying expressions and solving problems efficiently.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Write 32 +24 as a product of two factors using the gcf and the distributive property The correct answer and explanation is: To express 32+2432 + 24 as a product of two factors using the greatest common factor (GCF) and the distributive property, we begin by identifying the GCF of 32 and 24. Step 1: [&hellip;]<\/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-253420","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/253420","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=253420"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/253420\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=253420"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=253420"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=253420"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}