{"id":34573,"date":"2025-06-23T16:46:58","date_gmt":"2025-06-23T16:46:58","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=34573"},"modified":"2025-06-23T16:47:00","modified_gmt":"2025-06-23T16:47:00","slug":"use-the-prime-factor-trees-to-find-the-highest-common-factor-hcf-of-330-and-550","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/use-the-prime-factor-trees-to-find-the-highest-common-factor-hcf-of-330-and-550\/","title":{"rendered":"Use the prime factor trees to find the highest common factor (HCF) of 330 and 550"},"content":{"rendered":"\n<p>Use the prime factor trees to find the highest common factor (HCF) of 330 and 550<\/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>To find the highest common factor (HCF) of 330 and 550 using prime factor trees, follow these steps:<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Prime Factor Tree for 330<\/h3>\n\n\n\n<p>Start breaking down 330:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>330 is divisible by 2:<br>330 \u00f7 2 = 165<\/li>\n\n\n\n<li>165 is divisible by 3:<br>165 \u00f7 3 = 55<\/li>\n\n\n\n<li>55 is divisible by 5:<br>55 \u00f7 5 = 11<\/li>\n\n\n\n<li>11 is a prime number<\/li>\n<\/ul>\n\n\n\n<p>So, the prime factorization of 330 is:<br><strong>2 \u00d7 3 \u00d7 5 \u00d7 11<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Prime Factor Tree for 550<\/h3>\n\n\n\n<p>Now break down 550:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>550 is divisible by 2:<br>550 \u00f7 2 = 275<\/li>\n\n\n\n<li>275 is divisible by 5:<br>275 \u00f7 5 = 55<\/li>\n\n\n\n<li>55 is divisible by 5:<br>55 \u00f7 5 = 11<\/li>\n\n\n\n<li>11 is a prime number<\/li>\n<\/ul>\n\n\n\n<p>So, the prime factorization of 550 is:<br><strong>2 \u00d7 5 \u00d7 5 \u00d7 11<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Identify Common Prime Factors<\/h3>\n\n\n\n<p>Now compare the prime factors of both numbers:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>330: 2, 3, 5, 11<\/li>\n\n\n\n<li>550: 2, 5, 5, 11<\/li>\n<\/ul>\n\n\n\n<p>The common prime factors are:<br><strong>2, 5, and 11<\/strong><\/p>\n\n\n\n<p>We only include each common prime factor once when calculating the HCF. Multiply the common factors:<\/p>\n\n\n\n<p><strong>HCF = 2 \u00d7 5 \u00d7 11 = 110<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer: <strong>110<\/strong><\/h3>\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>The highest common factor (HCF) of two numbers is the largest number that divides both without leaving a remainder. One efficient method of finding the HCF is using prime factor trees. This method involves breaking down each number into its prime factors then identifying which factors are shared.<\/p>\n\n\n\n<p>For 330, we divide by the smallest prime number that fits. Since 330 is even, we divide by 2. That gives 165. Continuing, we divide 165 by 3 which gives 55. Next, 55 is divisible by 5 and that leaves 11 which is already prime. So the full factorization is 2, 3, 5, and 11.<\/p>\n\n\n\n<p>Next, for 550, we again start with 2 since it&#8217;s even. That gives 275. Then we divide by 5 to get 55, and again by 5 to get 11. So the factorization is 2, 5, 5, and 11.<\/p>\n\n\n\n<p>Now we compare the prime factors of both numbers. The numbers 2, 5, and 11 appear in both lists. Even though 550 has two 5s, we only take one for the purpose of finding the HCF. The HCF includes only the prime numbers that appear in both factorizations and only in the smallest power they appear in both.<\/p>\n\n\n\n<p>So multiplying the common factors \u2014 2, 5, and 11 \u2014 gives 110. This is the largest number that evenly divides both 330 and 550. Thus, the HCF of 330 and 550 is 110.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"722\" height=\"1024\" src=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner10-285.jpeg\" alt=\"\" class=\"wp-image-34574\" srcset=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner10-285.jpeg 722w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner10-285-212x300.jpeg 212w\" sizes=\"auto, (max-width: 722px) 100vw, 722px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Use the prime factor trees to find the highest common factor (HCF) of 330 and 550 The Correct Answer and Explanation is: To find the highest common factor (HCF) of 330 and 550 using prime factor trees, follow these steps: Step 1: Prime Factor Tree for 330 Start breaking down 330: So, the prime factorization [&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-34573","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/34573","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=34573"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/34573\/revisions"}],"predecessor-version":[{"id":34575,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/34573\/revisions\/34575"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=34573"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=34573"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=34573"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}