A divisor is a number that divides evenly into another number without leaving any remainder. If *n* is a multiple of *m*, then *m* is called a divisor of *n*. A number *n* is divisible by *m* if and only if *n* == 0 (mod *m*).

## Definition[]

If *m* and *n* are positive integers and *m* is a divisor of *n*, then *m* divides *n* and *n* is a multiple of *m*. More generally, it is said that *n* | *m*.

Sometimes divided by zero is included in this definition. This does not add much to the theory, because 0 does not divide any number except zero itself. In ring theory, *a* is called a **zero divisor** only if it is nonzero and if ab=0. Therefore, no nonzero integer is divisible by zero.

## General[]

Divisors can be positive as well as negative, but the term "divisor" usually refers to only positive divisors. For example, 10 has 6 divisors, namely 1, 2, 3, 4, 6 and 10, or 10 divisors when you include -1, -2, -3 −4, −6 and -10.

1 and -1 divide every integer. Every integer n is divisible by the number *n* itself and -*n*. Integers which have 2 and -2 as divisors are even numbers, while numbers without 2 or -2 as divisors are odd numbers.

A nontrivial divisor of *n *is a number which is a divisor of *n* other than 1, -1, *n*, and -*n*. A nonzero integer with at least one nontrivial divisor is known as a composite number. The prime numbers, 1 and -1 have no nontrivial divisors.