SOLUTION: Find the number of trailing zeros in M where M=201!-200!? answers 49,50,51,52

Question 550226: Find the number of trailing zeros in M where M=201!-200!? answers 49,50,51,52
Answer by fcabanski(1391) (Show Source): You can put this solution on YOUR website!
51

201! - 200! = 201*200! - 200! = 200*200!

To find the number of trailing zeros in any n! determine the number of times it is divisible by all smaller powers of 5.

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.

Ignore remainders

200/5 = 40 + 200/25=8 + 200/125=1 = 49.

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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