{"id":236032,"date":"2025-06-16T03:43:37","date_gmt":"2025-06-16T03:43:37","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=236032"},"modified":"2025-06-16T03:43:39","modified_gmt":"2025-06-16T03:43:39","slug":"make-three-different-factor-trees-for-48","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/16\/make-three-different-factor-trees-for-48\/","title":{"rendered":"make three different factor trees for 48"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">make three different factor trees for 48. Is the prime factorisation of 48 different in each case<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-0-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Factor Trees for 48<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Tree 1:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>48<br>\u2192 2 \u00d7 24<br>\u2192 2 \u00d7 (2 \u00d7 12)<br>\u2192 2 \u00d7 (2 \u00d7 (2 \u00d7 6))<br>\u2192 2 \u00d7 (2 \u00d7 (2 \u00d7 (2 \u00d7 3)))<br>\u2192 Prime factors: <strong>2 \u00d7 2 \u00d7 2 \u00d7 2 \u00d7 3<\/strong><\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Tree 2:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>48<br>\u2192 3 \u00d7 16<br>\u2192 3 \u00d7 (2 \u00d7 8)<br>\u2192 3 \u00d7 (2 \u00d7 (2 \u00d7 4))<br>\u2192 3 \u00d7 (2 \u00d7 (2 \u00d7 (2 \u00d7 2)))<br>\u2192 Prime factors: <strong>2 \u00d7 2 \u00d7 2 \u00d7 2 \u00d7 3<\/strong><\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Tree 3:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>48<br>\u2192 6 \u00d7 8<br>\u2192 (2 \u00d7 3) \u00d7 (2 \u00d7 4)<br>\u2192 (2 \u00d7 3) \u00d7 (2 \u00d7 (2 \u00d7 2))<br>\u2192 Prime factors: <strong>2 \u00d7 2 \u00d7 2 \u00d7 2 \u00d7 3<\/strong><\/li>\n<\/ul>\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 class=\"wp-block-paragraph\">Although the factor trees begin with different pairings, the process of breaking each composite number down to its simplest building blocks ultimately leads to the same set of prime numbers. This consistent result illustrates the <strong>Fundamental Theorem of Arithmetic<\/strong>, which states that each integer greater than one has a <strong>unique<\/strong> prime factorisation, regardless of how the factorisation is performed.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">In the case of 48, all paths converge on the same set of prime factors: four 2s and one 3. Arranged in order, the prime factorisation is:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>2\u2074 \u00d7 3<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The structure of the factor tree may vary in appearance or branching logic, but the outcome remains unchanged. This reinforces that prime factorisation is determined only by the properties of the number, not by the chosen order or method of breaking it down.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Different paths to the same conclusion serve to highlight flexibility in method and consistency in mathematical truth. Prime factorisation, though it can be approached in many ways, always leads to the same final expression for any given number.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner5-623.jpeg\" alt=\"\" class=\"wp-image-236033\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>make three different factor trees for 48. Is the prime factorisation of 48 different in each case The Correct Answer and Explanation is: Factor Trees for 48 Tree 1: Tree 2: Tree 3: Explanation Although the factor trees begin with different pairings, the process of breaking each composite number down to its simplest building blocks [&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-236032","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/236032","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=236032"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/236032\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=236032"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=236032"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=236032"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}