# Divisor

A natural number is called a **divisor** of a natural number if there is a natural number such that or, in other words, if is also a natural number (i.e divides ). See Divisibility for more information.

## Notation

A common notation to indicate a number is a divisor of another is . This means that divides .

See the main article on counting divisors. If is the prime factorization of , then the number of different divisors of is given by the formula . It is often useful to know that this expression grows slower than any positive power of as .
We also know that the product of the divisors of any integer is
Another useful idea is that is odd if and only if is a perfect square.

## Useful formulas

- If and are relatively prime, then