# Definition:Common Divisor/Real Numbers

## Definition

Let $S$ be a finite set of real numbers, that is:

$S = \set {x_1, x_2, \ldots, x_n: \forall k \in \N^*_n: x_k \in \R}$

Let $c \in \R$ such that $c$ divides all the elements of $S$, that is:

$\forall x \in S: c \divides x$

Then $c$ is a common divisor of all the elements in $S$.

## Also known as

The term common factor is also often found, meaning the same thing as common divisor.

In Euclid's The Elements, the term common measure is universally used for this concept.