Definition:Common Divisor/Integers

Definition

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

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

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

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

Then $c$ is a common divisor (or common factor) of all the elements in $S$.

Sources

• 1971: George E. Andrews: Number Theory ... (previous) ... (next): $\S 2.2$: Example $2.4$
• 1978: Thomas A. Whitelaw: An Introduction to Abstract Algebra ... (previous) ... (next): $\S 12$: Highest common factors and Euclid's algorithm