If N is the product of all positive integers less than 31, than what is the greatest integer k for which N/18^k is an integer?
Hi all, this was my approach for solving this.
Basically the question is asking us what is the highest power of 18 that can give us a number that is a factor of 31!
So remember 18 after prime factorization is (3^2)(2). Now there are going to be less factors of 3 in 31!, than factors of 2.
Therefore, lets find how many factors of 3 in 31! We can use this quick method
31/3^1 = 10
Sum = 14
Just ignore the remainders.
So we have that 3^14 must be the least. Now don't forget that 18 is 3^2k so k must be ONLY 7, because 2k will give us the 14.
Hence answer is (C)
Hope it helps
Bunuel could you please validate this one? Thank you