document.write( "Question 550226: Find the number of trailing zeros in M where M=201!-200!? answers 49,50,51,52 \n" ); document.write( "
Algebra.Com's Answer #358669 by fcabanski(1391)\"\" \"About 
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51


\n" ); document.write( "201! - 200! = 201*200! - 200! = 200*200!


\n" ); document.write( "To find the number of trailing zeros in any n! determine the number of times it is divisible by all smaller powers of 5.


\n" ); document.write( "The reason it works is that zeros happen whenever 10 is a factor, and 5 and 2 are factors of 10. Find the number of 5's that factor into the n! n, also the number of 5x5's and 5x5x5's etc.


\n" ); document.write( "Ignore remainders


\n" ); document.write( "200/5 = 40 + 200/25=8 + 200/125=1 = 49.


\n" ); document.write( "But this n! is multiplied by another number. Each of the zeros at the end of 200 will create a trailing 0. So it's 49+2 = 51.

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