Question 130014
First expand 50!


50!=50*49*48*47*46*...*3*2*1



Notice how 50! is made of the product of the numbers from 1 to 50, including the prime numbers from 1 to 50. So the prime numbers:


2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47,


are factors of the prime numbers that make up 50! and are factors of the composite numbers that make up 50! (for example 4=2*2, 24=2*2*2*3, and 32=2*2*2*2*2). Remember, any number can be represented as a product of primes.



So to find the number of primes that divide into 50!, simply count the number of primes from 1 to 50.



So there are 15 primes that divide into 50!