GRE Quant Flashcards Group 2 Quiz Problem

Can someone please explain this solution? Not sure how to solve this at all.

Hi,
Factors of 24 are 2223.
So it can be n^23 => 24 factors
N^3 * M^5 => 4
6=24 factors
N^1 * M^3 * L^2=243 =24 factors
N^1 * M^1 L^1 * O^2 =2223=24 factors
As 24 cannot. Be written as multiplication of 5 primes(either same or different) its not possible to have 5.