To factor the expression 60\u22123660 – 3660\u221236 using the Greatest Common Factor (GCF), let’s break it down step by step.<\/p>\n\n\n\n
Step 1: Find the GCF of 60 and 36<\/h3>\n\n\n\n
To begin, we need to determine the GCF of the two numbers, 60 and 36. The GCF is the largest number that divides both 60 and 36 evenly.<\/p>\n\n\n\n
- \n
- Prime Factorization of 60:<\/strong>\n
- \n
- 60 can be factored as 60=22\u00d73\u00d7560 = 2^2 \\times 3 \\times 560=22\u00d73\u00d75.<\/li>\n<\/ul>\n<\/li>\n\n\n\n
- Prime Factorization of 36:<\/strong>\n
- \n
- 36 can be factored as 36=22\u00d73236 = 2^2 \\times 3^236=22\u00d732.<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n
Step 2: Determine the Common Factors<\/h3>\n\n\n\n
From the factorizations:<\/p>\n\n\n\n
- \n
- The common factors between 60 and 36 are 222^222 and 333.<\/li>\n\n\n\n
- The GCF is therefore 22\u00d73=122^2 \\times 3 = 1222\u00d73=12.<\/li>\n<\/ul>\n\n\n\n
Step 3: Factor the Expression Using the GCF<\/h3>\n\n\n\n
Now, we can factor out the GCF of 12 from the original expression 60\u22123660 – 3660\u221236.60\u221236=12\u00d7(6012\u22123612)60 – 36 = 12 \\times \\left( \\frac{60}{12} – \\frac{36}{12} \\right)60\u221236=12\u00d7(1260\u200b\u22121236\u200b)60\u221236=12\u00d7(5\u22123)60 – 36 = 12 \\times (5 – 3)60\u221236=12\u00d7(5\u22123)60\u221236=12\u00d7260 – 36 = 12 \\times 260\u221236=12\u00d72<\/p>\n\n\n\n
Step 4: Simplify<\/h3>\n\n\n\n
Thus, the factored form of 60\u22123660 – 3660\u221236 is:60\u221236=12\u00d72=2460 – 36 = 12 \\times 2 = 2460\u221236=12\u00d72=24<\/p>\n\n\n\n
Explanation:<\/h3>\n\n\n\n
The process of factoring out the GCF involves finding the largest number that divides both terms in the expression. By recognizing that both 60 and 36 share a common factor of 12, we can simplify the expression and rewrite it as the product of 12 and the difference between 5 and 3, which is 2. This method helps in simplifying expressions, making it easier to handle mathematical problems and calculations.<\/p>\n\n\n\n
![\"\"](\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner6-970.jpeg\")
<\/figure>\n","protected":false},"excerpt":{"rendered":"Factor the expression using the GCF. 60 \u2013 36 = The Correct Answer and Explanation is: To factor the expression 60\u22123660 – 3660\u221236 using the Greatest Common Factor (GCF), let’s break it down step by step. Step 1: Find the GCF of 60 and 36 To begin, we need to determine the GCF of the […]<\/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-259455","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/259455","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=259455"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/259455\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=259455"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=259455"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=259455"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
- 36 can be factored as 36=22\u00d73236 = 2^2 \\times 3^236=22\u00d732.<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n