Divisor

Definition

Given two integers, $a,b\in\mathbb{Z}$, we say that $b$ divides $a$, or $b$ is a divisor of $a$, or $b$ is a factor of $a$ if there exists a third integer, $c\in\mathbb{Z}$ such that:

• $$a=bc$$

Formally, we say:

• Given $a,b\in\mathbb{Z}$, $b$ is a divisor of, factor of, or divides $a$ if $\exists c\in\mathbb{Z}[a=bc]$

Notes:

1. That we may also say $a$ is a multiple of $b$
2. The number $c$ may be called the co-factor of $b$ in $a$

See next

• GCD

See also

• Division algorithm