NOTE: CAN SOMEONE MOVE THIS QUESTION TO THE ALGEBRA SECTION? I posted here by mistake.

For any positive integer n, n > 1, the LENGTH of n is the number of positive primes (not necessarily distinct) whose product is n. For example, the length of 50 is 3 since 50 = (2)(5)(5).

Which of the following integers has length 3?

A. 3

B. 15

C. 60

D. 64

E. 105

I selected 60 but the correct answer is 105.

My Work:

60 = 15 * 2 * 2

I forgot that 15 can also be broken down a little more via prime factorization or the famous factor tree. I understand why my answer is wrong. Also, 15 is not a prime number. The question (like most recent posted applications) comes from the GMAT Review/Prep book (1997). BTW, I am not taking the GMAT. However, I find the given word problems interestingly enough to daily practice.

A. How would you tackle this problem?

B. What indication is there in the question itself pointing to the idea of prime factorization?