{"id":256673,"date":"2025-07-16T12:07:48","date_gmt":"2025-07-16T12:07:48","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=256673"},"modified":"2025-07-16T12:07:51","modified_gmt":"2025-07-16T12:07:51","slug":"explain-how-to-use-prime-factorization-to-find-the-gcf-of-90-and-84-without-drawing-venn-diagram","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/16\/explain-how-to-use-prime-factorization-to-find-the-gcf-of-90-and-84-without-drawing-venn-diagram\/","title":{"rendered":"Explain how to use prime factorization to find the GCF of 90 and 84 without drawing Venn diagram"},"content":{"rendered":"\n

Explain how to use prime factorization to find the GCF of 90 and 84 without drawing Venn diagram: How is the symbolic method similar to and different from the Venn diagram method of= ‘finding the GCF?<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

To find the GCF (Greatest Common Factor)<\/strong> of 90 and 84 using prime factorization<\/strong> (without using a Venn diagram), follow these steps:<\/p>\n\n\n\n

Step 1: Prime factorization of both numbers<\/h3>\n\n\n\n

90<\/strong>
90 \u00f7 2 = 45
45 \u00f7 3 = 15
15 \u00f7 3 = 5
5 \u00f7 5 = 1
So, the prime factorization of 90 is:
90 = 2 \u00d7 3 \u00d7 3 \u00d7 5<\/strong> or 2 \u00d7 3\u00b2 \u00d7 5<\/strong><\/p>\n\n\n\n

84<\/strong>
84 \u00f7 2 = 42
42 \u00f7 2 = 21
21 \u00f7 3 = 7
7 \u00f7 7 = 1
So, the prime factorization of 84 is:
84 = 2 \u00d7 2 \u00d7 3 \u00d7 7<\/strong> or 2\u00b2 \u00d7 3 \u00d7 7<\/strong><\/p>\n\n\n\n

Step 2: Identify common prime factors<\/h3>\n\n\n\n

Look for the prime numbers that appear in both<\/strong> factorizations.<\/p>\n\n\n\n

    \n
  • Both numbers have 2<\/strong>: 90 has one 2, and 84 has two 2s \u2192 take the lowest power<\/strong>, which is one 2.<\/li>\n\n\n\n
  • Both numbers have 3<\/strong>: 90 has two 3s, and 84 has one 3 \u2192 take the lowest power<\/strong>, which is one 3.<\/li>\n\n\n\n
  • 5 appears only in 90, and 7 appears only in 84 \u2192 do not include them.<\/li>\n<\/ul>\n\n\n\n

    Step 3: Multiply the common prime factors<\/h3>\n\n\n\n

    GCF = 2 \u00d7 3 = 6<\/strong><\/p>\n\n\n\n

    \n\n\n\n

    Explanation of Symbolic vs. Venn Diagram Method<\/h3>\n\n\n\n

    Both methods involve finding common prime factors<\/strong>. The symbolic method<\/strong> uses multiplication and exponents to list prime factors and compare powers. The Venn diagram method<\/strong> uses two circles to visually group shared and unshared primes. The overlapping part of the diagram shows common primes used to find the GCF.<\/p>\n\n\n\n

    The similarity<\/strong> is that both methods rely on identifying common primes<\/strong> and multiplying them to get the GCF. The difference<\/strong> is in the presentation: the symbolic method is more numerical and abstract, while the Venn diagram is visual and can be easier for learners who prefer diagrams. Both reach the same answer.<\/p>\n\n\n\n

    \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

    Explain how to use prime factorization to find the GCF of 90 and 84 without drawing Venn diagram: How is the symbolic method similar to and different from the Venn diagram method of= ‘finding the GCF? The Correct Answer and Explanation is: To find the GCF (Greatest Common Factor) of 90 and 84 using prime […]<\/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-256673","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/256673","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=256673"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/256673\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=256673"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=256673"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=256673"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}