{"id":38835,"date":"2025-06-26T13:42:38","date_gmt":"2025-06-26T13:42:38","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=38835"},"modified":"2025-06-26T13:42:46","modified_gmt":"2025-06-26T13:42:46","slug":"what-is-the-greatest-common-factor-gcf-of-32-and-48","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/what-is-the-greatest-common-factor-gcf-of-32-and-48\/","title":{"rendered":"What is the greatest common factor (GCF) of 32 and 48"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">What is the greatest common factor (GCF) of 32 and 48? A. 96 B. 16 C. 8 D. 32<\/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-vivid-cyan-blue-color\">The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Correct Answer: B. 16<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">To find the <strong>Greatest Common Factor (GCF)<\/strong> of 32 and 48, you need to determine the largest number that can divide <strong>both<\/strong> numbers exactly, with no remainder.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Step-by-step process:<\/strong><\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Prime Factorization<\/strong>\n<ul class=\"wp-block-list\">\n<li>32 = 2 \u00d7 2 \u00d7 2 \u00d7 2 \u00d7 2 = 2\u2075<\/li>\n\n\n\n<li>48 = 2 \u00d7 2 \u00d7 2 \u00d7 2 \u00d7 3 = 2\u2074 \u00d7 3<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Compare Common Prime Factors<\/strong><br>The prime factors they both share are powers of 2.\n<ul class=\"wp-block-list\">\n<li>32 has five 2s<\/li>\n\n\n\n<li>48 has four 2s<br>So, they both share four 2s, or 2\u2074.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Multiply Shared Factors<\/strong><br>2\u2074 = 2 \u00d7 2 \u00d7 2 \u00d7 2 = 16<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">So, the greatest number that divides both 32 and 48 is <strong>16<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Why not the other options?<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>A. 96<\/strong>: 96 is larger than both 32 and 48. A common factor must be <strong>less than or equal<\/strong> to the smallest number, which is 32. So 96 cannot be the GCF.<\/li>\n\n\n\n<li><strong>C. 8<\/strong>: 8 is a common factor of 32 and 48, but it is not the greatest. 16 is larger and still divides both numbers.<\/li>\n\n\n\n<li><strong>D. 32<\/strong>: 32 is a factor of 32 but <strong>not<\/strong> of 48. 48 \u00f7 32 = 1.5, which is not a whole number.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Conclusion<\/strong><br>The GCF is the largest number that can divide both 32 and 48 without leaving a remainder. The correct answer is <strong>16<\/strong> because it is the highest number that divides both evenly. It plays an important role in simplifying fractions and solving ratio problems. Understanding how to find the GCF helps strengthen skills in number theory and arithmetic.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>What is the greatest common factor (GCF) of 32 and 48? A. 96 B. 16 C. 8 D. 32 The correct answer and explanation is: Correct Answer: B. 16 To find the Greatest Common Factor (GCF) of 32 and 48, you need to determine the largest number that can divide both numbers exactly, with no [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-38835","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/38835","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=38835"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/38835\/revisions"}],"predecessor-version":[{"id":38854,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/38835\/revisions\/38854"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=38835"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=38835"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=38835"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}