Common divisor
= Common divisor
{title2=$d\mid a,\ d\mid b$}
A positive <integer> $d$ is a common divisor of <integers> $a,b$ when $d\mid a$ and $d\mid b$. For positive $a,b$, their largest <common divisor> is their <greatest common divisor>. The identity $a=qb+r$ implies that $a,b$ and $b,r$ have the same positive <common divisors>, because $r=a-qb$ and $a=qb+r$.