If 100!/30^n is an integer, which of the following is the greatest possible value of n?
Options:
(A) 28
(B) 24
(C) 20
(D) 15
(E) 10 Stream of consciousness first, then make a decision:
user
30^n = 2^n * 3^n * 5^n
100! has 97 2's, 48 3's and 24 5's
Since each of 2, 3 and 5 is required to form 30 and there are only 24 5's there can only be 24 30's in 100!
Thus, the answer is (B).
assistant