{"id":250198,"date":"2025-07-10T08:19:00","date_gmt":"2025-07-10T08:19:00","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=250198"},"modified":"2025-07-10T08:19:03","modified_gmt":"2025-07-10T08:19:03","slug":"what-is-5632-distributive-property-to-factor-out-the-greatest-common-factor","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/10\/what-is-5632-distributive-property-to-factor-out-the-greatest-common-factor\/","title":{"rendered":"what is 56+32 distributive property to factor out the greatest common factor."},"content":{"rendered":"\n<p>what is 56+32 distributive property to factor out the greatest common factor.<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To apply the distributive property and factor out the greatest common factor (GCF) for the expression 56+3256 + 3256+32, we follow these steps:<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Identify the GCF<\/h3>\n\n\n\n<p>First, we need to find the GCF of the two numbers, 56 and 32.<\/p>\n\n\n\n<p>The factors of 56 are:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>1, 2, 4, 7, 8, 14, 28, 56.<\/li>\n<\/ul>\n\n\n\n<p>The factors of 32 are:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>1, 2, 4, 8, 16, 32.<\/li>\n<\/ul>\n\n\n\n<p>The greatest common factor (GCF) is the largest number that appears in both lists of factors. In this case, the GCF of 56 and 32 is 8.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Apply the distributive property<\/h3>\n\n\n\n<p>Now, we use the distributive property to factor out the GCF. The distributive property states that: a+b=c(a+b)a + b = c(a + b)a+b=c(a+b)<\/p>\n\n\n\n<p>where ccc is the GCF. So, we factor out 8 from both terms in the expression 56+3256 + 3256+32: 56+32=8(7+4)56 + 32 = 8(7 + 4)56+32=8(7+4)<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Verify the result<\/h3>\n\n\n\n<p>To verify that the factoring is correct, we can expand the expression 8(7+4)8(7 + 4)8(7+4) back out: 8(7+4)=8\u00d77+8\u00d74=56+328(7 + 4) = 8 \\times 7 + 8 \\times 4 = 56 + 328(7+4)=8\u00d77+8\u00d74=56+32<\/p>\n\n\n\n<p>This confirms that our factoring is correct.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer:<\/h3>\n\n\n\n<p>The factored form of 56+3256 + 3256+32 is: 56+32=8(7+4)56 + 32 = 8(7 + 4)56+32=8(7+4)<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>We applied the distributive property by first identifying the greatest common factor (GCF) of 56 and 32, which is 8. By factoring out 8, we simplified the expression to 8(7+4)8(7 + 4)8(7+4), which is equivalent to the original sum. This shows how the distributive property can help factor expressions efficiently by identifying common factors.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner6-92.jpeg\" alt=\"\" class=\"wp-image-250213\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>what is 56+32 distributive property to factor out the greatest common factor. The Correct Answer and Explanation is: To apply the distributive property and factor out the greatest common factor (GCF) for the expression 56+3256 + 3256+32, we follow these steps: Step 1: Identify the GCF First, we need to find the GCF of the [&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-250198","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/250198","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=250198"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/250198\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=250198"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=250198"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=250198"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}