{"id":90199,"date":"2025-06-01T10:22:45","date_gmt":"2025-06-01T10:22:45","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=90199"},"modified":"2025-06-01T10:22:45","modified_gmt":"2025-06-01T10:22:45","slug":"consider-the-following-number-n-6374-1793-x625-317-x313-49","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/consider-the-following-number-n-6374-1793-x625-317-x313-49\/","title":{"rendered":"Consider the following number :\nn = [(6374) 1793 \u00d7(625) 317 \u00d7(313) 49"},"content":{"rendered":"

Consider the following number :
\nn = [(6374)1793<\/sup>\u00d7(625)317<\/sup>\u00d7(313)49<\/sup>]
\nWhich one of the following is the digit at the unit place of n ?<\/p>\n

[amp_mcq option1=”0″ option2=”1″ option3=”2″ option4=”5″ correct=”option1″]<\/p>\n

\n
\n
This question was previously asked in<\/div>\n
UPSC CAPF – 2017<\/div>\n<\/div>\n
Download PDF<\/a>Attempt Online<\/a><\/div>\n<\/div>\n
\nThe correct option is A.
\n<\/section>\n
\nTo find the unit digit of n = [(6374)^1793 \u00d7 (625)^317 \u00d7 (313)^49], we only need to find the unit digit of the product of the unit digits of each term raised to its power.
\n– Unit digit of (6374)^1793 is the unit digit of 4^1793. The pattern of unit digits for powers of 4 is 4, 6, 4, 6… The unit digit is 4 for odd exponents and 6 for even exponents. Since 1793 is odd, the unit digit of 4^1793 is 4.
\n– Unit digit of (625)^317 is the unit digit of 5^317. The unit digit of any positive integer power of 5 is always 5. So, the unit digit of 5^317 is 5.
\n– Unit digit of (313)^49 is the unit digit of 3^49. The pattern of unit digits for powers of 3 is 3, 9, 7, 1, 3, 9, 7, 1… The pattern repeats every 4 powers. We find the remainder of 49 divided by 4: 49 = 12 * 4 + 1. The remainder is 1. The unit digit is the same as the 1st power’s unit digit, which is 3. So, the unit digit of 3^49 is 3.
\nThe unit digit of n is the unit digit of (Unit digit of 4^1793) * (Unit digit of 5^317) * (Unit digit of 3^49) = Unit digit of (4 * 5 * 3).
\n4 * 5 = 20. The unit digit of 20 is 0.
\nThe unit digit of (20 * 3) is the unit digit of 60.
\nThe unit digit is 0.
\n<\/section>\n
\nThe unit digit of a product is solely determined by the unit digits of the numbers being multiplied. Calculating the full value of the expression is unnecessary. Understanding the cyclical nature of unit digits for powers of integers is key to solving this problem.
\n<\/section>\n","protected":false},"excerpt":{"rendered":"

Consider the following number : n = [(6374)1793\u00d7(625)317\u00d7(313)49] Which one of the following is the digit at the unit place of n ? [amp_mcq option1=”0″ option2=”1″ option3=”2″ option4=”5″ correct=”option1″] This question was previously asked in UPSC CAPF – 2017 Download PDFAttempt Online The correct option is A. To find the unit digit of n = … <\/p>\n

Detailed SolutionConsider the following number :
\nn = [(6374) 1793 \u00d7(625) 317 \u00d7(313) 49<\/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":[1085],"tags":[1101,1102],"class_list":["post-90199","post","type-post","status-publish","format-standard","hentry","category-upsc-capf","tag-1101","tag-quantitative-aptitude-and-reasoning","no-featured-image-padding"],"yoast_head":"\nConsider the following number : n = [(6374) 1793 \u00d7(625) 317 \u00d7(313) 49<\/title>\n<meta name=\"description\" content=\"The correct option is A. To find the unit digit of n = [(6374)^1793 \u00d7 (625)^317 \u00d7 (313)^49], we only need to find the unit digit of the product of the unit digits of each term raised to its power. - Unit digit of (6374)^1793 is the unit digit of 4^1793. The pattern of unit digits for powers of 4 is 4, 6, 4, 6... The unit digit is 4 for odd exponents and 6 for even exponents. Since 1793 is odd, the unit digit of 4^1793 is 4. - Unit digit of (625)^317 is the unit digit of 5^317. The unit digit of any positive integer power of 5 is always 5. So, the unit digit of 5^317 is 5. - Unit digit of (313)^49 is the unit digit of 3^49. The pattern of unit digits for powers of 3 is 3, 9, 7, 1, 3, 9, 7, 1... The pattern repeats every 4 powers. We find the remainder of 49 divided by 4: 49 = 12 * 4 + 1. The remainder is 1. The unit digit is the same as the 1st power's unit digit, which is 3. So, the unit digit of 3^49 is 3. The unit digit of n is the unit digit of (Unit digit of 4^1793) * (Unit digit of 5^317) * (Unit digit of 3^49) = Unit digit of (4 * 5 * 3). 4 * 5 = 20. The unit digit of 20 is 0. The unit digit of (20 * 3) is the unit digit of 60. The unit digit is 0.\" \/>\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\/consider-the-following-number-n-6374-1793-x625-317-x313-49\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Consider the following number : n = [(6374) 1793 \u00d7(625) 317 \u00d7(313) 49\" \/>\n<meta property=\"og:description\" content=\"The correct option is A. To find the unit digit of n = [(6374)^1793 \u00d7 (625)^317 \u00d7 (313)^49], we only need to find the unit digit of the product of the unit digits of each term raised to its power. - Unit digit of (6374)^1793 is the unit digit of 4^1793. The pattern of unit digits for powers of 4 is 4, 6, 4, 6... The unit digit is 4 for odd exponents and 6 for even exponents. Since 1793 is odd, the unit digit of 4^1793 is 4. - Unit digit of (625)^317 is the unit digit of 5^317. The unit digit of any positive integer power of 5 is always 5. So, the unit digit of 5^317 is 5. - Unit digit of (313)^49 is the unit digit of 3^49. The pattern of unit digits for powers of 3 is 3, 9, 7, 1, 3, 9, 7, 1... The pattern repeats every 4 powers. We find the remainder of 49 divided by 4: 49 = 12 * 4 + 1. The remainder is 1. The unit digit is the same as the 1st power's unit digit, which is 3. So, the unit digit of 3^49 is 3. The unit digit of n is the unit digit of (Unit digit of 4^1793) * (Unit digit of 5^317) * (Unit digit of 3^49) = Unit digit of (4 * 5 * 3). 4 * 5 = 20. The unit digit of 20 is 0. The unit digit of (20 * 3) is the unit digit of 60. The unit digit is 0.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/consider-the-following-number-n-6374-1793-x625-317-x313-49\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T10:22:45+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":"Consider the following number : n = [(6374) 1793 \u00d7(625) 317 \u00d7(313) 49","description":"The correct option is A. To find the unit digit of n = [(6374)^1793 \u00d7 (625)^317 \u00d7 (313)^49], we only need to find the unit digit of the product of the unit digits of each term raised to its power. - Unit digit of (6374)^1793 is the unit digit of 4^1793. The pattern of unit digits for powers of 4 is 4, 6, 4, 6... The unit digit is 4 for odd exponents and 6 for even exponents. Since 1793 is odd, the unit digit of 4^1793 is 4. - Unit digit of (625)^317 is the unit digit of 5^317. The unit digit of any positive integer power of 5 is always 5. So, the unit digit of 5^317 is 5. - Unit digit of (313)^49 is the unit digit of 3^49. The pattern of unit digits for powers of 3 is 3, 9, 7, 1, 3, 9, 7, 1... The pattern repeats every 4 powers. We find the remainder of 49 divided by 4: 49 = 12 * 4 + 1. The remainder is 1. The unit digit is the same as the 1st power's unit digit, which is 3. So, the unit digit of 3^49 is 3. The unit digit of n is the unit digit of (Unit digit of 4^1793) * (Unit digit of 5^317) * (Unit digit of 3^49) = Unit digit of (4 * 5 * 3). 4 * 5 = 20. The unit digit of 20 is 0. The unit digit of (20 * 3) is the unit digit of 60. The unit digit is 0.","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\/consider-the-following-number-n-6374-1793-x625-317-x313-49\/","og_locale":"en_US","og_type":"article","og_title":"Consider the following number : n = [(6374) 1793 \u00d7(625) 317 \u00d7(313) 49","og_description":"The correct option is A. To find the unit digit of n = [(6374)^1793 \u00d7 (625)^317 \u00d7 (313)^49], we only need to find the unit digit of the product of the unit digits of each term raised to its power. - Unit digit of (6374)^1793 is the unit digit of 4^1793. The pattern of unit digits for powers of 4 is 4, 6, 4, 6... The unit digit is 4 for odd exponents and 6 for even exponents. Since 1793 is odd, the unit digit of 4^1793 is 4. - Unit digit of (625)^317 is the unit digit of 5^317. The unit digit of any positive integer power of 5 is always 5. So, the unit digit of 5^317 is 5. - Unit digit of (313)^49 is the unit digit of 3^49. The pattern of unit digits for powers of 3 is 3, 9, 7, 1, 3, 9, 7, 1... The pattern repeats every 4 powers. We find the remainder of 49 divided by 4: 49 = 12 * 4 + 1. The remainder is 1. The unit digit is the same as the 1st power's unit digit, which is 3. So, the unit digit of 3^49 is 3. The unit digit of n is the unit digit of (Unit digit of 4^1793) * (Unit digit of 5^317) * (Unit digit of 3^49) = Unit digit of (4 * 5 * 3). 4 * 5 = 20. The unit digit of 20 is 0. The unit digit of (20 * 3) is the unit digit of 60. The unit digit is 0.","og_url":"https:\/\/exam.pscnotes.com\/mcq\/consider-the-following-number-n-6374-1793-x625-317-x313-49\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T10:22:45+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\/consider-the-following-number-n-6374-1793-x625-317-x313-49\/","url":"https:\/\/exam.pscnotes.com\/mcq\/consider-the-following-number-n-6374-1793-x625-317-x313-49\/","name":"Consider the following number : n = [(6374) 1793 \u00d7(625) 317 \u00d7(313) 49","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T10:22:45+00:00","dateModified":"2025-06-01T10:22:45+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"The correct option is A. To find the unit digit of n = [(6374)^1793 \u00d7 (625)^317 \u00d7 (313)^49], we only need to find the unit digit of the product of the unit digits of each term raised to its power. - Unit digit of (6374)^1793 is the unit digit of 4^1793. The pattern of unit digits for powers of 4 is 4, 6, 4, 6... The unit digit is 4 for odd exponents and 6 for even exponents. Since 1793 is odd, the unit digit of 4^1793 is 4. - Unit digit of (625)^317 is the unit digit of 5^317. The unit digit of any positive integer power of 5 is always 5. So, the unit digit of 5^317 is 5. - Unit digit of (313)^49 is the unit digit of 3^49. The pattern of unit digits for powers of 3 is 3, 9, 7, 1, 3, 9, 7, 1... The pattern repeats every 4 powers. We find the remainder of 49 divided by 4: 49 = 12 * 4 + 1. The remainder is 1. The unit digit is the same as the 1st power's unit digit, which is 3. So, the unit digit of 3^49 is 3. The unit digit of n is the unit digit of (Unit digit of 4^1793) * (Unit digit of 5^317) * (Unit digit of 3^49) = Unit digit of (4 * 5 * 3). 4 * 5 = 20. The unit digit of 20 is 0. The unit digit of (20 * 3) is the unit digit of 60. The unit digit is 0.","breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/consider-the-following-number-n-6374-1793-x625-317-x313-49\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/consider-the-following-number-n-6374-1793-x625-317-x313-49\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/consider-the-following-number-n-6374-1793-x625-317-x313-49\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/exam.pscnotes.com\/mcq\/"},{"@type":"ListItem","position":2,"name":"UPSC CAPF","item":"https:\/\/exam.pscnotes.com\/mcq\/category\/upsc-capf\/"},{"@type":"ListItem","position":3,"name":"Consider the following number : n = [(6374) 1793 \u00d7(625) 317 \u00d7(313) 49"}]},{"@type":"WebSite","@id":"https:\/\/exam.pscnotes.com\/mcq\/#website","url":"https:\/\/exam.pscnotes.com\/mcq\/","name":"MCQ and Quiz for Exams","description":"","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/exam.pscnotes.com\/mcq\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"Person","@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209","name":"rawan239","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/761a7274f9cce048fa5b921221e7934820d74514df93ef195a9d22af0c1c9001?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/761a7274f9cce048fa5b921221e7934820d74514df93ef195a9d22af0c1c9001?s=96&d=mm&r=g","caption":"rawan239"},"sameAs":["https:\/\/exam.pscnotes.com"],"url":"https:\/\/exam.pscnotes.com\/mcq\/author\/rawan239\/"}]}},"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/90199","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/comments?post=90199"}],"version-history":[{"count":0,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/90199\/revisions"}],"wp:attachment":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/media?parent=90199"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/categories?post=90199"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/tags?post=90199"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}