{"id":43055,"date":"2025-06-29T13:18:19","date_gmt":"2025-06-29T13:18:19","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=43055"},"modified":"2025-06-29T13:18:21","modified_gmt":"2025-06-29T13:18:21","slug":"what-is-the-greatest-common-factor-of-100-and-50","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/what-is-the-greatest-common-factor-of-100-and-50\/","title":{"rendered":"What is the greatest common factor of 100 and 50"},"content":{"rendered":"\n<p>What is the greatest common factor of 100 and 50?<\/p>\n\n\n\n<p><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>The greatest common factor (GCF) of 100 and 50 is <strong>50<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>To find the greatest common factor, we need to list the factors of both numbers and identify the largest number that appears in both lists.<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Factors of 100<\/strong>: The factors of 100 are all the numbers that divide into 100 exactly. These factors are:\n<ul class=\"wp-block-list\">\n<li>1, 2, 4, 5, 10, 20, 25, 50, 100<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Factors of 50<\/strong>: The factors of 50 are all the numbers that divide into 50 exactly. These factors are:\n<ul class=\"wp-block-list\">\n<li>1, 2, 5, 10, 25, 50<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n<p>Now, by comparing the two lists of factors, we can see that the common factors are:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>1, 2, 5, 10, 25, 50<\/li>\n<\/ul>\n\n\n\n<p>The greatest of these common factors is <strong>50<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Another Method: Prime Factorization<\/h3>\n\n\n\n<p>Another way to find the GCF is by using prime factorization. We break both numbers down into their prime factors:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Prime factorization of 100<\/strong>:\n<ul class=\"wp-block-list\">\n<li>100 = 2 \u00d7 2 \u00d7 5 \u00d7 5 = 22\u00d7522^2 \\times 5^2<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Prime factorization of 50<\/strong>:\n<ul class=\"wp-block-list\">\n<li>50 = 2 \u00d7 5 \u00d7 5 = 21\u00d7522^1 \\times 5^2<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<p>To find the GCF, we take the lowest power of each prime factor that appears in both factorizations:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The lowest power of 2 is 212^1.<\/li>\n\n\n\n<li>The lowest power of 5 is 525^2.<\/li>\n<\/ul>\n\n\n\n<p>Therefore, the GCF is 21\u00d752=2\u00d725=502^1 \\times 5^2 = 2 \\times 25 = 50.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Conclusion:<\/h3>\n\n\n\n<p>Both methods show that the greatest common factor of 100 and 50 is 50. This is the largest number that can divide both 100 and 50 without leaving a remainder.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>What is the greatest common factor of 100 and 50? The correct answer and explanation is: The greatest common factor (GCF) of 100 and 50 is 50. Explanation: To find the greatest common factor, we need to list the factors of both numbers and identify the largest number that appears in both lists. Now, by [&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-43055","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/43055","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=43055"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/43055\/revisions"}],"predecessor-version":[{"id":43060,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/43055\/revisions\/43060"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=43055"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=43055"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=43055"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}