{"id":253917,"date":"2025-07-12T08:00:38","date_gmt":"2025-07-12T08:00:38","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=253917"},"modified":"2025-07-12T08:00:40","modified_gmt":"2025-07-12T08:00:40","slug":"find-the-prime-factor-by-breaking-by-breaking-down-into-smaller-factors-no-are-3245468522","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/12\/find-the-prime-factor-by-breaking-by-breaking-down-into-smaller-factors-no-are-3245468522\/","title":{"rendered":"find the prime factor by breaking by breaking down into smaller factors no are 32,45,468,522"},"content":{"rendered":"\n<p>find the prime factor by breaking by breaking down into smaller factors no are 32,45,468,522<\/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>Let&#8217;s break down the prime factors for each of these numbers:<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">1. <strong>32:<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Start with dividing by 2, the smallest prime.<br>32 \u00f7 2 = 16<br>16 \u00f7 2 = 8<br>8 \u00f7 2 = 4<br>4 \u00f7 2 = 2<br>2 \u00f7 2 = 1<\/li>\n<\/ul>\n\n\n\n<p>Thus, the prime factorization of 32 is: <strong>2 \u00d7 2 \u00d7 2 \u00d7 2 \u00d7 2<\/strong> or <strong>2^5<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">2. <strong>45:<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Start by dividing by 3, the smallest prime.<br>45 \u00f7 3 = 15<br>15 \u00f7 3 = 5<br>5 \u00f7 5 = 1<\/li>\n<\/ul>\n\n\n\n<p>Thus, the prime factorization of 45 is: <strong>3 \u00d7 3 \u00d7 5<\/strong> or <strong>3^2 \u00d7 5<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">3. <strong>468:<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Start by dividing by 2.<br>468 \u00f7 2 = 234<br>234 \u00f7 2 = 117<\/li>\n\n\n\n<li>Now divide by 3.<br>117 \u00f7 3 = 39<br>39 \u00f7 3 = 13<\/li>\n\n\n\n<li>Now, 13 is a prime number.<\/li>\n<\/ul>\n\n\n\n<p>Thus, the prime factorization of 468 is: <strong>2 \u00d7 2 \u00d7 3 \u00d7 3 \u00d7 13<\/strong> or <strong>2^2 \u00d7 3^2 \u00d7 13<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">4. <strong>522:<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Start by dividing by 2.<br>522 \u00f7 2 = 261<\/li>\n\n\n\n<li>Now divide by 3.<br>261 \u00f7 3 = 87<br>87 \u00f7 3 = 29<\/li>\n\n\n\n<li>29 is a prime number.<\/li>\n<\/ul>\n\n\n\n<p>Thus, the prime factorization of 522 is: <strong>2 \u00d7 3 \u00d7 3 \u00d7 29<\/strong> or <strong>2 \u00d7 3^2 \u00d7 29<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>Prime factorization is the process of breaking a number down into the prime numbers that multiply together to give the original number. Prime numbers are integers greater than 1 that are divisible only by 1 and themselves.<\/p>\n\n\n\n<p>To factorize a number, we begin by testing divisibility by the smallest primes (starting with 2) and continue dividing by the primes until all factors are prime. In the case of even numbers like 32 and 468, the number is divisible by 2 repeatedly. For other numbers, such as 45, we use primes like 3 or 5 as divisibility rules apply (e.g., 3 divides a number if the sum of its digits is divisible by 3).<\/p>\n","protected":false},"excerpt":{"rendered":"<p>find the prime factor by breaking by breaking down into smaller factors no are 32,45,468,522 The correct answer and explanation is: Let&#8217;s break down the prime factors for each of these numbers: 1. 32: Thus, the prime factorization of 32 is: 2 \u00d7 2 \u00d7 2 \u00d7 2 \u00d7 2 or 2^5. 2. 45: Thus, [&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-253917","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/253917","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=253917"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/253917\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=253917"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=253917"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=253917"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}