{"id":169472,"date":"2024-11-19T09:20:26","date_gmt":"2024-11-19T09:20:26","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=169472"},"modified":"2024-11-19T09:20:28","modified_gmt":"2024-11-19T09:20:28","slug":"what-is-the-greatest-perfect-square-that-is-a-factor-of-147","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/11\/19\/what-is-the-greatest-perfect-square-that-is-a-factor-of-147\/","title":{"rendered":"What is the greatest perfect square that is a factor of 147"},"content":{"rendered":"\n<p>What is the greatest perfect square that is a factor of 147?<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n<p>To find the greatest perfect square that is a factor of 147, we need to start by finding the prime factorization of 147.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Prime Factorization of 147<\/h3>\n\n\n\n<p>Start by dividing 147 by the smallest prime, which is 2. Since 147 is an odd number, it is not divisible by 2.<\/p>\n\n\n\n<p>Next, check for divisibility by 3:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The sum of the digits of 147 is ( 1 + 4 + 7 = 12 ), which is divisible by 3.<\/li>\n\n\n\n<li>So, divide 147 by 3:<br>[<br>147 \\div 3 = 49<br>]<br>Now, we have ( 147 = 3 \\times 49 ).<\/li>\n<\/ul>\n\n\n\n<p>Next, factor 49. Since 49 is ( 7^2 ), we have:<br>[<br>49 = 7 \\times 7<br>]<br>Thus, the complete prime factorization of 147 is:<br>[<br>147 = 3 \\times 7^2<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Identify the Perfect Square Factors<\/h3>\n\n\n\n<p>A perfect square is a number whose prime factors all appear with even exponents. To find the greatest perfect square factor of 147, we examine the prime factorization:<br>[<br>147 = 3^1 \\times 7^2<br>]<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The factor ( 3^1 ) has an odd exponent, so it cannot contribute to a perfect square.<\/li>\n\n\n\n<li>The factor ( 7^2 ) has an even exponent, so it can contribute to a perfect square.<\/li>\n<\/ul>\n\n\n\n<p>Thus, the greatest perfect square factor is ( 7^2 = 49 ).<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Verify<\/h3>\n\n\n\n<p>We now check if 49 is a factor of 147:<br>[<br>147 \\div 49 = 3<br>]<br>Since 3 is an integer, 49 is indeed a factor of 147.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Conclusion<\/h3>\n\n\n\n<p>The greatest perfect square that is a factor of 147 is ( \\boxed{49} ).<\/p>\n","protected":false},"excerpt":{"rendered":"<p>What is the greatest perfect square that is a factor of 147? The Correct Answer and Explanation is : To find the greatest perfect square that is a factor of 147, we need to start by finding the prime factorization of 147. Step 1: Prime Factorization of 147 Start by dividing 147 by the smallest [&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-169472","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/169472","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=169472"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/169472\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=169472"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=169472"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=169472"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}