Greatest Common Divisor is Associative

Theorem
Let $a, b, c \in \Z$.

Then:


 * $\gcd \set {a, \gcd \set {b, c} } = \gcd \set {\gcd \set {a, b}, c}$

where $\gcd$ denotes the greatest common divisor.

Proof
Follows directly from GCD from Prime Decomposition and Min Operation is Associative.

Also see

 * Lowest Common Multiple is Associative