let be a prime number and be a positive integer for all

a) list all distinct divisors of 32

1,2,4,8,16,32

5+1 = 6 divisors

b) how many distinct divisors does have?

a+1 divisors

c) how many distinct divisors does have?

divisors

d) how many distinct divisors does 60 have?

using prime factorization

so it has

here is the one I don't know how to solve

e) What is the smallest positive integer with exactly 100 distinct divisors?