Divisor
In mathematics a divisor of an integer
, also called a factor of
, is an integer that can be multiplied by some other integer to produce
. An integer
is divisible by another integer
if
is a factor of
, so that dividing
by
leaves no remainder.
Definition
Two versions of the definition of a divisor are commonplace:
For integers
and
, it is said that
divides
,
is a divisor of
, or
is a multiple of
, and this is written as

As before, but with the additional constraint
. Under this definition, the statement
does not hold.
In the remainder of this article, which definition is applied is indicated where this is significant.
General
Divisors can be negative as well as positive, although sometimes the term is restricted to positive divisors. For example, there are six divisors of 4; they are 1, 2, 4, −1, −2, and −4, but only the positive ones (1, 2, and 4) would usually be mentioned.
1 and −1 divide (are divisors of) every integer. Every integer (and its negation) is a divisor of itself. Every integer is a divisor of 0. Integers divisible by 2 are called even, and numbers not divisible by 2 are called odd.