Integer m has 4 different prime factors and n has 3 different prime factors. If m and n has the greatest common factor of 15, how many different prime factors does mn have?  Choices
A) 4
B) 5
C) 6
D) 7
E) 8

Rationale: as m and n has gcf of 15 , 3 * 5 should be common factor for both m and n . m = 3 * 5 * p 1 * p 2 n = 3 * 5 * p 3 mn = 3 ^ 2 * 5 ^ 2 * p 1 * p 2 * p 3 mn has prime numbers of 3,5 , p 1 , p 2 p 3 b
Answer: B