Definition:Common Divisor/Integers
< Definition:Common Divisor(Redirected from Definition:Common Divisor of Integers)
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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): $\text {2-2}$ Divisibility: Example $\text {2-4}$
- 1978: Thomas A. Whitelaw: An Introduction to Abstract Algebra ... (previous) ... (next): $\S 12$: Highest common factors and Euclid's algorithm
- 1980: David M. Burton: Elementary Number Theory (revised ed.) ... (previous) ... (next): Chapter $2$: Divisibility Theory in the Integers: $2.2$ The Greatest Common Divisor
