Greatest Common Divisor is Associative

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

Then $\gcd \{a, \gcd \{ b, c\} \} = \gcd \{ \gcd \{ a, b\}, c\}$.

Proof
It follows directly from GCD from Prime Decomposition and Min is Associative.

Also see

 * Lowest Common Multiple is Associative