Divisor

Definition

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

• [math]a=bc[/math]

Formally, we say:

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

Notes:

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

See next

• GCD

See also

• Division algorithm