Q: If 100!/30^n is an integer, which of the following is the greatest possible value of n?\nOptions:\n(A) 28\n(B) 24\n(C) 20\n(D) 15\n(E) 10 Let's give some random thoughts before answering.
User
30^n = 2^n * 3^n * 5^n\n100! has 97 2's, 48 3's and 24 5's\nSince 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!
Therefore, the answer is (B).
Assistant