How many different primes appear in the prime factorization of $20!/18!$? (Reminder: The number n! is the product of the integers from 1 to n. For example 5! = 5*4*3*2*1 = 120)
20! ==2 , 2 , 2 , 2 , 2 , 2 , 2 , 2 , 2 , 2 , 2 , 2 , 2 , 2 , 2 , 2 , 2 , 2 , 3 , 3 , 3 , 3 , 3 , 3 , 3 , 3 , 5 , 5 , 5 , 5 , 7 , 7 , 11 , 13 , 17 , 19 , Total Prime Factors = 36
Distinct Number of Factors = 8
18! ==2 , 2 , 2 , 2 , 2 , 2 , 2 , 2 , 2 , 2 , 2 , 2 , 2 , 2 , 2 , 2 , 3 , 3 , 3 , 3 , 3 , 3 , 3 , 3 , 5 , 5 , 5 , 7 , 7 , 11 , 13 , 17 , Total Prime Factors = 32
Distinct Number of Factors = 7
20! / 18! ==2 , 2 , 5 , 19 , Total Prime Factors = 4
Distinct Number of Factors = 3
