Claim:Gcd(a,b) is greater than all other common divisors of a and b

Claim (see proof):

For all [math]a, b, c \href{/cs2800/wiki/index.php/%E2%88%88}{∈} ℕ [/math], if [math]c \href{/cs2800/wiki/index.php/%E2%9D%98}{❘} a [/math] and [math]c \href{/cs2800/wiki/index.php/%E2%9D%98}{❘} b [/math], then [math]c ≤ \href{/cs2800/wiki/index.php/Gcd}{gcd}(a,b) [/math].