Number of Divisors

Number of Divisors

## Formula

If:

$$N=p_1^{a_1}p_2^{a_2}\cdots p_k^{a_k}$$

where $p_1,p_2,\ldots,p_k$ are distinct primes, then the number of positive divisors of $$n$$ is:

$$d(N)=(a_1+1)(a_2+1)\cdots(a_k+1)$$

## Usage

- Used in counting problems involving selection of prime-power factors.