X, Y, and Z are different prime numbers. The product X^2*Y*Z is divisible by how many different positive numbers? Choose one
A) 4 B) 6 C) 8 D) 9 E) 12

Rationale: the exponents of x ^ 2 * y * z are 2 , 1 , and 1 . the number of factors is ( 2 + 1 ) ( 1 + 1 ) ( 1 + 1 ) = 12 the answer is e .
Answer: E