And in general, if you have a prime factorization:

\(n = 2^x 3^a 5^b\)

-the number of positive divisors of n will be (x+1)*(a+1)*(b+1)

-the number of odd positive divisors of n will be (a+1)*(b+1)

-the number of even positive divisors of n will be x*(a+1)*(b+1)

This will be true no matter what primes you have in your factorization - the odd primes don't need to be 3 and 5 - and regardless of how many primes you have in the prime factorization (I used two odd primes just for illustration).

_________________

GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com