factorial divided by a smaller factorial to the n power

Question

This is the question I am asking: Compute the greatest integer n for which (6!)^n is a factor of 60!.

This is an AMC style question as I am practicing for it. I tried to find the amount of 6's in 60! and got 11, but it was incorrect. Any help?

Answer 1

Count primes instead of the largest number. Usually, the largest prime has the least amount of numbers. So count the 5's. 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60. There are 12 5's and 2 more 5's from 25 and 50 so it is 12 + 2 = 14.