As the GCF of m and n is 15 = 3*5, m and n both must have 3 and 5 as their prime factors. Hence, the other two prime factors of m and the third prime factor n must be different from each other.lenagmat wrote: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?
It says m has 4 different prime factors and n has 3Anurag@Gurome wrote:As the GCF of m and n is 15 = 3*5, m and n both must have 3 and 5 as their prime factors. Hence, the other two prime factors of both m and n must be different from each other.lenagmat wrote: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?
Hence, the different prime factors of mn are 3, 5, two other prime factors of m and two other prime factors of n.
Hence, number of different prime factors of mn = 2 + 2 + 2 = 6
The correct answer is C.
Alternatively, we could pick some numbers that satisfy the given conditions.lenagmat wrote: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?
A). 4
B). 5
C). 6
D). 7
E). 8
If m and n have a GCF of 15, they both share a prime of 3 and 5. Thus, m has 2 prime factors that differ from those of n and n has 1 other prime factor that differs from those of m.lenagmat wrote: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?
A). 4
B). 5
C). 6
D). 7
E). 8
