gnet, that's a good catch. I thought of it in terms of distinct prime factors, and if the OA stands as A, it looks like the question also assumes that it is in fact distinct prime factors that matter. thanks mp2437. I knew you were talking about distinct prime factors only :) I think the actual GMA...

Hi, this is an old thread, already well explained by Vivek, but I thought I would throw in here another formula/appproach to such questions, where we need to determine the exact power of a given prime p which divides n! (you will though need to know or learn how to convert a decimal to a different b...

(30!) / 3^k 30/3 will give max. 10 multiples 30/(3)^2 will give max. 3 multiples 30/(3)^3 will give max 1. multiple Add the above to get max. 14 multiples (multiplicity) of prime number 3 in the prime factorization of 30! --------- Let's try another (a simpler one). 5! / 2^k 5/2 --> max. 2 multiples...