Divisor (of an integer or of a polynomial)

A divisor of an integer $a$ is an integer $b$ which divides $a$ without remainder. In other words, a divisor of the integer $a$ is an integer $b$ such that, for a certain integer $c$, the equality $a=bc$ holds. A divisor of a polynomial $A(x)$ is a polynomial $B(x)$ that divides $A(x)$ without remainder (cf. Division). More generally, in an arbitrary ring $A$, a divisor of an element $a \in A$ is an element $b\in A$ such that $a=bc$ for a certain $c\in A$.