X, Y, and Z are different prime numbers. The product X^3*Y^2*Z^1 is divisible by how many different positive numbers?  Choose the correct option.
A) 24
B) 30
C) 36
D) 42
E) 48
The exponents of X^3*Y^2*Z^1 are 3, 2, and 1.   The number of factors is (3+1)(2+1)(1+1) = 24   The answer is 24.
<result>A</result>
X, Y, and Z are different prime numbers. The product X^3*Y^2*Z^1 is divisible by how many different positive numbers?