Question

How do you find the number of factors of a number?

Answer 1

If the prime factorization of `n∈N` is

`n=\prod_{k=1} p_k^{a_k}`

then the number of divisors of `n` is

`\prod_{k=1} (a_k+1)`

For example `36=3^2*2^2` the number of divisors is

`(2+1)*(2+1)=9`

which are

`1 | 2 | 3 | 4 | 6 | 9 | 12 | 18 | 36`