Suppose n is a positive integer such that 6n has exactly 9 positive divisors.

How many prime numbers are divisors of 6n?

Guest Mar 13, 2021

#1**0 **

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. :))

=^._.^=

catmg Mar 13, 2021