{"id":93249,"date":"2025-06-01T11:45:52","date_gmt":"2025-06-01T11:45:52","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=93249"},"modified":"2025-06-01T11:45:52","modified_gmt":"2025-06-01T11:45:52","slug":"what-is-the-smallest-number-which-when-multiplied-by-9-gives-the-prod","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/what-is-the-smallest-number-which-when-multiplied-by-9-gives-the-prod\/","title":{"rendered":"What is the smallest number, which when multiplied by 9 gives the prod"},"content":{"rendered":"

What is the smallest number, which when multiplied by 9 gives the product having the digit 5 only in all places ?<\/p>\n

[amp_mcq option1=”9528395″ option2=”61728395″ option3=”12345675″ option4=”59382716″ correct=”option2″]<\/p>\n

\n
\n
This question was previously asked in<\/div>\n
UPSC CISF-AC-EXE – 2023<\/div>\n<\/div>\n
Download PDF<\/a>Attempt Online<\/a><\/div>\n<\/div>\n
\nWe are looking for the smallest number, say ‘x’, such that when multiplied by 9, the product consists only of the digit 5. Let the product be P. So, 9 * x = P, where P is a number like 5, 55, 555, 5555, etc.
\nFor P to be divisible by 9, the sum of its digits must be divisible by 9. If P consists only of the digit 5, the sum of its digits is 5 multiplied by the number of digits. For this sum to be divisible by 9, the number of digits (all 5s) must be a multiple of 9.
\nThe smallest number of 5s that is a multiple of 9 is 9. So, the smallest possible product P is 555,555,555 (nine 5s).
\nNow, we find x by dividing P by 9:
\nx = 555,555,555 \/ 9
\nx = 61,728,395
\nComparing this with the given options, option B matches this value.
\n<\/section>\n
\n– A number is divisible by 9 if the sum of its digits is divisible by 9.
\n– To find the smallest such number ‘x’, the product P must be the smallest number consisting only of 5s that is divisible by 9.
\n– The smallest number of 5s required for the sum of digits to be divisible by 9 is nine 5s (since 9 * 5 = 45, which is divisible by 9).
\n<\/section>\n
\nThe calculation 555,555,555 \u00f7 9 can be done using long division or by recognizing patterns. Dividing a repdigit of ‘n’ digits by 9 follows a specific pattern. For example, 111…1 (n times) divided by 9 gives 0.111…1. Here, we have nine 5s. Dividing 111,111,111 by 9 gives 12,345,679. So, 555,555,555 = 5 * 111,111,111. Therefore, 555,555,555 \/ 9 = 5 * (111,111,111 \/ 9) = 5 * 12,345,679 = 61,728,395.
\n<\/section>\n","protected":false},"excerpt":{"rendered":"

What is the smallest number, which when multiplied by 9 gives the product having the digit 5 only in all places ? [amp_mcq option1=”9528395″ option2=”61728395″ option3=”12345675″ option4=”59382716″ correct=”option2″] This question was previously asked in UPSC CISF-AC-EXE – 2023 Download PDFAttempt Online We are looking for the smallest number, say ‘x’, such that when multiplied by … <\/p>\n

Detailed SolutionWhat is the smallest number, which when multiplied by 9 gives the prod<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1089],"tags":[1105,1102],"class_list":["post-93249","post","type-post","status-publish","format-standard","hentry","category-upsc-cisf-ac-exe","tag-1105","tag-quantitative-aptitude-and-reasoning","no-featured-image-padding"],"yoast_head":"\nWhat is the smallest number, which when multiplied by 9 gives the prod<\/title>\n<meta name=\"description\" content=\"We are looking for the smallest number, say 'x', such that when multiplied by 9, the product consists only of the digit 5. Let the product be P. So, 9 * x = P, where P is a number like 5, 55, 555, 5555, etc. For P to be divisible by 9, the sum of its digits must be divisible by 9. If P consists only of the digit 5, the sum of its digits is 5 multiplied by the number of digits. For this sum to be divisible by 9, the number of digits (all 5s) must be a multiple of 9. The smallest number of 5s that is a multiple of 9 is 9. So, the smallest possible product P is 555,555,555 (nine 5s). Now, we find x by dividing P by 9: x = 555,555,555 \/ 9 x = 61,728,395 Comparing this with the given options, option B matches this value. - A number is divisible by 9 if the sum of its digits is divisible by 9. - To find the smallest such number 'x', the product P must be the smallest number consisting only of 5s that is divisible by 9. - The smallest number of 5s required for the sum of digits to be divisible by 9 is nine 5s (since 9 * 5 = 45, which is divisible by 9).\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/exam.pscnotes.com\/mcq\/what-is-the-smallest-number-which-when-multiplied-by-9-gives-the-prod\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"What is the smallest number, which when multiplied by 9 gives the prod\" \/>\n<meta property=\"og:description\" content=\"We are looking for the smallest number, say 'x', such that when multiplied by 9, the product consists only of the digit 5. Let the product be P. So, 9 * x = P, where P is a number like 5, 55, 555, 5555, etc. For P to be divisible by 9, the sum of its digits must be divisible by 9. If P consists only of the digit 5, the sum of its digits is 5 multiplied by the number of digits. For this sum to be divisible by 9, the number of digits (all 5s) must be a multiple of 9. The smallest number of 5s that is a multiple of 9 is 9. So, the smallest possible product P is 555,555,555 (nine 5s). Now, we find x by dividing P by 9: x = 555,555,555 \/ 9 x = 61,728,395 Comparing this with the given options, option B matches this value. - A number is divisible by 9 if the sum of its digits is divisible by 9. - To find the smallest such number 'x', the product P must be the smallest number consisting only of 5s that is divisible by 9. - The smallest number of 5s required for the sum of digits to be divisible by 9 is nine 5s (since 9 * 5 = 45, which is divisible by 9).\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/what-is-the-smallest-number-which-when-multiplied-by-9-gives-the-prod\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T11:45:52+00:00\" \/>\n<meta name=\"author\" content=\"rawan239\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"rawan239\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"What is the smallest number, which when multiplied by 9 gives the prod","description":"We are looking for the smallest number, say 'x', such that when multiplied by 9, the product consists only of the digit 5. 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Now, we find x by dividing P by 9: x = 555,555,555 \/ 9 x = 61,728,395 Comparing this with the given options, option B matches this value. - A number is divisible by 9 if the sum of its digits is divisible by 9. - To find the smallest such number 'x', the product P must be the smallest number consisting only of 5s that is divisible by 9. - The smallest number of 5s required for the sum of digits to be divisible by 9 is nine 5s (since 9 * 5 = 45, which is divisible by 9).","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/exam.pscnotes.com\/mcq\/what-is-the-smallest-number-which-when-multiplied-by-9-gives-the-prod\/","og_locale":"en_US","og_type":"article","og_title":"What is the smallest number, which when multiplied by 9 gives the prod","og_description":"We are looking for the smallest number, say 'x', such that when multiplied by 9, the product consists only of the digit 5. 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Now, we find x by dividing P by 9: x = 555,555,555 \/ 9 x = 61,728,395 Comparing this with the given options, option B matches this value. - A number is divisible by 9 if the sum of its digits is divisible by 9. - To find the smallest such number 'x', the product P must be the smallest number consisting only of 5s that is divisible by 9. - The smallest number of 5s required for the sum of digits to be divisible by 9 is nine 5s (since 9 * 5 = 45, which is divisible by 9).","og_url":"https:\/\/exam.pscnotes.com\/mcq\/what-is-the-smallest-number-which-when-multiplied-by-9-gives-the-prod\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T11:45:52+00:00","author":"rawan239","twitter_card":"summary_large_image","twitter_misc":{"Written by":"rawan239","Est. reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/exam.pscnotes.com\/mcq\/what-is-the-smallest-number-which-when-multiplied-by-9-gives-the-prod\/","url":"https:\/\/exam.pscnotes.com\/mcq\/what-is-the-smallest-number-which-when-multiplied-by-9-gives-the-prod\/","name":"What is the smallest number, which when multiplied by 9 gives the prod","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T11:45:52+00:00","dateModified":"2025-06-01T11:45:52+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"We are looking for the smallest number, say 'x', such that when multiplied by 9, the product consists only of the digit 5. Let the product be P. So, 9 * x = P, where P is a number like 5, 55, 555, 5555, etc. For P to be divisible by 9, the sum of its digits must be divisible by 9. If P consists only of the digit 5, the sum of its digits is 5 multiplied by the number of digits. For this sum to be divisible by 9, the number of digits (all 5s) must be a multiple of 9. The smallest number of 5s that is a multiple of 9 is 9. So, the smallest possible product P is 555,555,555 (nine 5s). 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