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

How many prime numbers are divisors of 6n?

 Mar 13, 2021
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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. :))

 

=^._.^=

 Mar 13, 2021

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