Greatest Common Divisor is Associative
Jump to navigation
Jump to search
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.