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). Given this information, which of the following integers has a length of 3?

A. 3

B. 15

C. 60

D. 64

E. 105

I said 15 • 2 • 2 = 30 • 2 = 60.

The correct answer is 105. Why is my answer incorrect?