SOLUTION: how many 0s at the end of 95!?

Question 388588: how many 0s at the end of 95!?
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
It suffices to count the number of 5's in 95! since there will be enough 2's to make multiples of 10.

The multiples of 5 less than or equal to 95 are 5, 10, 15, ..., 95, so there are 19 multiples of 5. The multiples of 25 are 25, 50, 75, so 3 "additional" 5's, so there are 22 5's in the factorization of 95!. Therefore there are 22 zeroes at the end of 95!.

(The faster algorithm is to repeatedly divide by 5, i.e. 95/5 = 19, 19/5 = 3, 19+3 = 22)
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