find the greatest number which divides 225 and 2425 leaving remainder 5 in each case<\/p>\n\n\n\n
The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n Correct Answer: 20<\/strong><\/p>\n\n\n\n To find the greatest number that divides both 225 and 2425 leaving a remainder of 5 in each case, start by understanding the concept involved.<\/p>\n\n\n\n If a number divides 225 and 2425 leaving a remainder of 5 in both cases, then subtract 5 from each of the numbers. This is because the actual number that divides both must divide the differences:<\/p>\n\n\n\n Now, the required number must exactly divide both 220 and 2420. That means the required number is a common divisor of 220 and 2420.<\/p>\n\n\n\n To find the greatest such number, calculate the Highest Common Factor (HCF)<\/strong> or Greatest Common Divisor (GCD)<\/strong> of 220 and 2420.<\/p>\n\n\n\n 220 = 2 \u00d7 2 \u00d7 5 \u00d7 11 = 2\u00b2 \u00d7 5 \u00d7 11<\/strong> Now find the common prime factors:<\/p>\n\n\n\n So, But remember, we subtracted 5 earlier, so this 220 is the number that exactly divides<\/strong> both (225 – 5) and (2425 – 5). Hence, the greatest number<\/strong> that divides both 225<\/strong> and 2425<\/strong>, leaving a remainder of 5<\/strong>, is:<\/p>\n\n\n\n Answer: 220<\/strong><\/p>\n\n\n\n However, the question asks for the greatest number which divides<\/strong> 225 and 2425 leaving remainder 5. So the number must be less than both 225 and 2425<\/strong>, and divide the differences 220 and 2420<\/strong>. So now we double-check:<\/p>\n\n\n\n Find the HCF of 220 and 2420:<\/p>\n\n\n\n Therefore, HCF = 220<\/strong><\/p>\n\n\n\n Final Answer: 220<\/strong><\/p>\n\n\n\n (Note: earlier I incorrectly wrote 20 in the final answer \u2014 correct value is 220<\/strong>)<\/p>\n","protected":false},"excerpt":{"rendered":" find the greatest number which divides 225 and 2425 leaving remainder 5 in each case The correct answer and explanation is: Correct Answer: 20 Explanation: To find the greatest number that divides both 225 and 2425 leaving a remainder of 5 in each case, start by understanding the concept involved. If a number divides 225 […]<\/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-38570","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/38570","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=38570"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/38570\/revisions"}],"predecessor-version":[{"id":38571,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/38570\/revisions\/38571"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=38570"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=38570"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=38570"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Explanation:<\/h3>\n\n\n\n
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Step 1: Prime Factorization<\/h3>\n\n\n\n
2420 = 2 \u00d7 2 \u00d7 5 \u00d7 11 \u00d7 11 = 2\u00b2 \u00d7 5 \u00d7 11\u00b2<\/strong><\/p>\n\n\n\n\n
HCF = 2\u00b2 \u00d7 5 \u00d7 11 = 4 \u00d7 5 \u00d7 11 = 220<\/strong><\/p>\n\n\n\n\n