document.write( "Question 1182542: Find the last non-zero digit of 50! \n" ); document.write( "

Algebra.Com's Answer #812622 by ikleyn(52787) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "In web-page\r
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\n" ); document.write( "\n" ); document.write( "https://www.quora.com/What-is-the-first-non-zero-digit-in-50-factorial-50-How-did-you-get-the-answer-without-a-calculator#:~:text=The%20answer%20is%202%2C%20see,compute%20the%20factorization%20of%2050!\r
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\n" ); document.write( "\n" ); document.write( "you can find different solutions for any taste.\r
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\n" ); document.write( "\n" ); document.write( "The ANSWER is 2.\r
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\n" ); document.write( "\n" ); document.write( "Even better form solution, with examples, including the case 50!, is under this link\r
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\n" ); document.write( "\n" ); document.write( "https://www.justquant.com/numbertheory/how-to-find-last-non-zero-digit-in-a-factorial/\r
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document.write( "Also, a good idea is to present 50! as the product of five groups of numbers\r\n" );
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document.write( "    50! = (1*2*3*4*. . .*9*10) * (11*12*13*. . .*19*20) * (21*22*23*. . .*29*30) * (31*32*33*. . .*39*40) * (41*42*43*. . .*49*50)\r\n" );
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document.write( "It is clear that the last non-zero digit of 50! is the product of last non-zero digits of all five groups.\r\n" );
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document.write( "Regarding 1st group, 10! = 3628800;  the last non-zero digit is 8.\r\n" );
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document.write( "Regarding 2nd group, (11*12*13*. . . *18*19*20) = 670442572800;  the last non-zero digit is 8.\r\n" );
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document.write( "Regarding 3rd group, (21*22*23*. . . *28*29*30) = 109027350432000;  the last non-zero digit is 2.\r\n" );
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document.write( "Regarding 4th group, (31*32*33*. . . *38*39*40) = 3075990524006400;  the last non-zero digit is 4.\r\n" );
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document.write( "Regarding 5th group, (41*42*43*. . . *48*49*50) = 37276043023296000;  the last non-zero digit is 6.\r\n" );
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document.write( "Now,  the product of the last non-zero digits in these groups is  8*8*2*4*6 = 3072;\r\n" );
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document.write( "so, my DIRECT EMPIRICAL EXPERIMENT  C O N F I R M S  that the last non-zero digit in the number 50!  is  .\r\n" );
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\n" ); document.write( "\n" ); document.write( "Thanks to my MS EXCEL, making these boring calculations for me easy, fast and with no errors ( ! )\r
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