didnot understand

There are two possible types of numbers that satisfy the given information.

1) the number is in the form xy, where x and y are different prime numbers
2) the number is in the form x³, where x is a prime number

From there, it's a matter of listing and counting (as @Carcass has done)

Cheers,
Brent

In GRE, they mention that different factors. In this question they didn't mention that, so carcass didn't mention 9 for example.
9 factors are 1, 9, 3, 3. So, why carcass didn't repeat counting 3 two times?
Forget now about the formula, because I understand it.

I'm popping up years later because I was deeply confused on this. Adding to the explanations that use exponents to calculate the number of factors (case 2), here are a few examples of why 3^3 is included, despite it seemingly conflicting with the logic in case 1.

Using the formula xy with x and y being odd primes, to find four factors we use the formula adding 1 to each exponent and multiplying to find the total number of factors.

Thus, in the case of, say, 15, which in prime factorization is 3^1 5^1, the number of factors are (1+1) (1+1) = 4

Keeping with this formula xy = odd integer, 27 is included in this list because its factors xy could be listed as 3^3 y^0. We calculate the factors as (3+1)(0+1) = 4.
(as a reminder, any integer to the power of zero = 1)

This is why 9 and 25 aren't included, because 3^2 y^0 = (2+1) x (0+1) = 3

I am still uncertain how/why two apparently conflicting logics are used here, but keeping with the "formula" rather than listing these out, 27 is included, making the answer 17 instead of 16.

The question didn't necessarily specify "distinct" factors, but it took a lot of liberty in interpretation.