{"id":10391,"date":"2022-04-05T17:41:05","date_gmt":"2022-04-05T12:11:05","guid":{"rendered":"https:\/\/mathemerize.com\/?p=10391"},"modified":"2022-06-04T19:47:24","modified_gmt":"2022-06-04T14:17:24","slug":"check-whether-6n-can-end-with-the-digit-0-or-any-n-in-n","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/check-whether-6n-can-end-with-the-digit-0-or-any-n-in-n\/","title":{"rendered":"Check whether \\(6^n\\) can end with the digit 0 or any n \\(\\in\\) N."},"content":{"rendered":"<h2>Solution :<\/h2>\n<p>If the number \\(6^n\\) ends with the digit zero. Then it is divisible by 5.<\/p>\n<p>Therefore, the prime factors of \\(6^n\\) contains the prime number 5. This is not possible because the only primes in the factors of \\(6^n\\) are 2 and 3 and the uniqueness of the fundamental theorem of arithmetic guarantees that there are no other prime in the factors of \\(6^n\\).<\/p>\n<p>So, there is no value of n in natural numbers for which \\(6^n\\) ends with the digit zero.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Solution : If the number \\(6^n\\) ends with the digit zero. Then it is divisible by 5. Therefore, the prime factors of \\(6^n\\) contains the prime number 5. This is not possible because the only primes in the factors of \\(6^n\\) are 2 and 3 and the uniqueness of the fundamental theorem of arithmetic guarantees &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathemerize.com\/check-whether-6n-can-end-with-the-digit-0-or-any-n-in-n\/\"> <span class=\"screen-reader-text\">Check whether \\(6^n\\) can end with the digit 0 or any n \\(\\in\\) N.<\/span> Read More &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[43,909],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.12 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Check whether \\(6^n\\) can end with the digit 0 or any n \\(\\in\\) N. - Mathemerize<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathemerize.com\/check-whether-6n-can-end-with-the-digit-0-or-any-n-in-n\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Check whether \\(6^n\\) can end with the digit 0 or any n \\(\\in\\) N. - Mathemerize\" \/>\n<meta property=\"og:description\" content=\"Solution : If the number (6^n) ends with the digit zero. Then it is divisible by 5. Therefore, the prime factors of (6^n) contains the prime number 5. This is not possible because the only primes in the factors of (6^n) are 2 and 3 and the uniqueness of the fundamental theorem of arithmetic guarantees &hellip; Check whether (6^n) can end with the digit 0 or any n (in) N. 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Then it is divisible by 5. Therefore, the prime factors of (6^n) contains the prime number 5. This is not possible because the only primes in the factors of (6^n) are 2 and 3 and the uniqueness of the fundamental theorem of arithmetic guarantees &hellip; Check whether (6^n) can end with the digit 0 or any n (in) N. 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