isn't it going to be the product of the first 100 primes?
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?
ok I read a similar problem. It's not the product of the 1st 100 primes.
you have
$n = \displaystyle{\prod_{k=1}^N}p_k^{a_k}$
You want to find $N$ and the $a_k$ such that
$\displaystyle{\prod_{k=1}^N}a_k=100$
and
$n$ is minimized.
I'll have to think about how to solve this one.