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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 $6n$?

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

 Jun 28, 2015

Best Answer 

 #1
avatar+128079 
+16

I'll answer the second one, first....I believe that "n"  = 6    thus 6n  = 6(6) = 36

 

The positive divisors are   1, 2, 3, 4, 6, 9, 12, 18 and 36

 

So...the number of prime divisors of "6n"  is just  ... two .....  [ 2 and 3  ]

 

 

 Jun 28, 2015
 #1
avatar+128079 
+16
Best Answer

I'll answer the second one, first....I believe that "n"  = 6    thus 6n  = 6(6) = 36

 

The positive divisors are   1, 2, 3, 4, 6, 9, 12, 18 and 36

 

So...the number of prime divisors of "6n"  is just  ... two .....  [ 2 and 3  ]

 

 

CPhill Jun 28, 2015

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