{"id":45261,"date":"2025-07-01T04:47:01","date_gmt":"2025-07-01T04:47:01","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=45261"},"modified":"2025-07-01T04:47:03","modified_gmt":"2025-07-01T04:47:03","slug":"write-the-above-numbers-in-prime-factors-2-2","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/write-the-above-numbers-in-prime-factors-2-2\/","title":{"rendered":"Write the above numbers in prime factors 2.2"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\"> Given: 70 300 2.1 Write the above numbers in prime factors 2.2 Hence determine the LCM and HCF of 70 and 300<\/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<h3 class=\"wp-block-heading\">2.1 Prime Factorization<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Prime factorization of 70:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Start by dividing 70 by the smallest prime number, which is 2:<br>70\u00f72=3570 \\div 2 = 3570\u00f72=35<br>So, 70 = 2 \u00d7 35.<\/li>\n\n\n\n<li>Next, divide 35 by the smallest prime number, which is 5:<br>35\u00f75=735 \\div 5 = 735\u00f75=7.<br>So, 35 = 5 \u00d7 7.<\/li>\n\n\n\n<li>7 is a prime number, so we stop here.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Thus, the prime factorization of 70 is:<br>70=2\u00d75\u00d7770 = 2 \u00d7 5 \u00d7 770=2\u00d75\u00d77.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Prime factorization of 300:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Start by dividing 300 by 2:<br>300\u00f72=150300 \\div 2 = 150300\u00f72=150.<br>So, 300 = 2 \u00d7 150.<\/li>\n\n\n\n<li>Divide 150 by 2 again:<br>150\u00f72=75150 \\div 2 = 75150\u00f72=75.<br>So, 150 = 2 \u00d7 75.<\/li>\n\n\n\n<li>Divide 75 by 3 (since 75 is divisible by 3):<br>75\u00f73=2575 \\div 3 = 2575\u00f73=25.<br>So, 75 = 3 \u00d7 25.<\/li>\n\n\n\n<li>Now, divide 25 by 5:<br>25\u00f75=525 \\div 5 = 525\u00f75=5.<br>So, 25 = 5 \u00d7 5.<\/li>\n\n\n\n<li>5 is prime, so we stop here.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Thus, the prime factorization of 300 is:<br>300=22\u00d73\u00d752300 = 2^2 \u00d7 3 \u00d7 5^2300=22\u00d73\u00d752.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">2.2 Determining the LCM and HCF<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>HCF (Highest Common Factor)<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">To find the HCF, identify the common prime factors with the smallest powers:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Prime factors of 70: 21\u00d751\u00d7712^1 \\times 5^1 \\times 7^121\u00d751\u00d771.<\/li>\n\n\n\n<li>Prime factors of 300: 22\u00d731\u00d7522^2 \\times 3^1 \\times 5^222\u00d731\u00d752.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">The common prime factors are 2 and 5. The lowest powers of these factors are:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>For 2: 212^121.<\/li>\n\n\n\n<li>For 5: 515^151.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Thus, the HCF is:<br>HCF=21\u00d751=2\u00d75=10HCF = 2^1 \\times 5^1 = 2 \\times 5 = 10HCF=21\u00d751=2\u00d75=10.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>LCM (Least Common Multiple)<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">To find the LCM, take all prime factors from both numbers with the highest powers:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Prime factors of 70: 21\u00d751\u00d7712^1 \\times 5^1 \\times 7^121\u00d751\u00d771.<\/li>\n\n\n\n<li>Prime factors of 300: 22\u00d731\u00d7522^2 \\times 3^1 \\times 5^222\u00d731\u00d752.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">The LCM is obtained by taking the highest powers of all prime factors:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>For 2: 222^222.<\/li>\n\n\n\n<li>For 3: 313^131.<\/li>\n\n\n\n<li>For 5: 525^252.<\/li>\n\n\n\n<li>For 7: 717^171.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Thus, the LCM is:<br>LCM=22\u00d731\u00d752\u00d771=4\u00d73\u00d725\u00d77=2100LCM = 2^2 \\times 3^1 \\times 5^2 \\times 7^1 = 4 \\times 3 \\times 25 \\times 7 = 2100LCM=22\u00d731\u00d752\u00d771=4\u00d73\u00d725\u00d77=2100.<\/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<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>HCF of 70 and 300<\/strong>: 10.<\/li>\n\n\n\n<li><strong>LCM of 70 and 300<\/strong>: 2100.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">The <strong>HCF<\/strong> is the largest number that divides both 70 and 300. It is found by considering the common factors between the two numbers and selecting the smallest powers of those factors. The <strong>LCM<\/strong> is the smallest number that both 70 and 300 can divide into, and it is found by taking all prime factors and using the largest powers of each factor.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"852\" height=\"1024\" src=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner8-18.jpeg\" alt=\"\" class=\"wp-image-45262\" srcset=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner8-18.jpeg 852w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner8-18-250x300.jpeg 250w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner8-18-768x923.jpeg 768w\" sizes=\"auto, (max-width: 852px) 100vw, 852px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Given: 70 300 2.1 Write the above numbers in prime factors 2.2 Hence determine the LCM and HCF of 70 and 300 The Correct Answer and Explanation is: 2.1 Prime Factorization Prime factorization of 70: Thus, the prime factorization of 70 is:70=2\u00d75\u00d7770 = 2 \u00d7 5 \u00d7 770=2\u00d75\u00d77. Prime factorization of 300: Thus, the prime [&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-45261","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/45261","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=45261"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/45261\/revisions"}],"predecessor-version":[{"id":45263,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/45261\/revisions\/45263"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=45261"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=45261"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=45261"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}