How to check what maximum power of prime number can divide a factorial number exactly?

If the number by which the factorial number has to be divided is a prime number i.e p and the maximum power of p is n. Let the factorial no. is N

We can check the maximum power of p by

n= [N/p] + [N/p2] + [N/p3] + ........................


Let 72! be the number and we have to find maximum power of 5 which can divide 72! exactly:

Therefore,

n=[72/5] + [72/25] = 14 + 2 = 16.