How many positive divisors of 30! are prime?
We could prime factorize the numbers below 30 and get the list 2,3,5,7,11,13,17,19,23,29
and that is \(\boxed{10\text{ numbers}}\)
Because a prime number is a number that can not be divisible by any number except for itself and one, you can just list the prime numbers under and/or equal to 30. Every composite, or non-prime, is divisible by at least two prime numbers.
