If n is the product of 2, 3, and a two-digit prime number...

[rrmm1989]

If n is the product of 2, 3, and a two-digit prime number, how many of its factors are greater than 6?

This question is from Manhattan GMAT's "Foundations of GMAT Math" book.

I understand why the answer is four. One way to answer this question is to simply plug in a two-digit prime number and look at its factors.

However, I can also use rules to determine that three of n's factors must be greater than six: 1 x n, 2 x two-digit prime number, and 3 x two-digit prime number. However, is there a rule that I'm missing that indicates why 6 x two-digit prime number must be a factor of n?

Thanks.

[RonPurewal]

Hi,
From now on, please post in the appropriate folder. (This question belongs in the MGMAT non-CAT math folder.)

Here, 6*prime = 3*2*prime is the value of n itself"”"”which is most certainly a factor of n. (Every number is a factor of itself.)