Wednesday, April 26, 2017

discrete mathematics - Determine the number of 0 digits at the end of 100!

I got this question, and I'm totally lost as to how I solve it!
Any help is appreciated :)



When 100! is written out in full, it equals
100! = 9332621...000000.

Without using a calculator, determine the number of 0 digits at the end of this number



EDIT:
Just want to confirm this is okay --



I got 24 by splitting products into 2 cases 1) multiples of 10 and 2) multiples of 5
Case I
(1*3*4*6*7*8*9*10)(100,000,000,000)--> 12 zeroes



Similarly got 12 zeroes for Case 2.




So 24 in total? Is that correct?

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