Suppose n is a positive integer such that 6n has exactly 9 positive divisors.
How many prime numbers are divisors of 6n?
The number of factors is (a+1)(b+1)... you can google it if you don't know.
a is the number of that paticular prime factor.
So for 9 factors. (a+1)(b+1) = 9
so both a and b must be 2.
6 = 2*3
So we need two factors of 2, and two factors of 3.
2*2*3*3 = 36.
There are only two prime factors of 36, 2 and 3.
I hope this helped. :))