Greatest Common Divisor of Set of Integers/Examples/39, 42, 54

Example of Greatest Common Divisor of Set of Integers

Let $S = \set {39, 42, 54}$.

The greatest common divisor of $S$ is:

$\map \gcd S = 3$

Proof

This theorem requires a proof. In particular: To do this formally, we need to first prove that $\gcd \set {a, b, c} = \gcd \set {\gcd \set {a, b}, c}$ or something similar You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{ProofWanted}} from the code. If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page.

Sources

• 1980: David M. Burton: Elementary Number Theory (revised ed.) ... (previous) ... (next): Chapter $2$: Divisibility Theory in the Integers: $2.3$ The Euclidean Algorithm