> [!NOTE] Theorem > Let $a,b$ be [[Integers|integers]] not both zero. Let $d$ be a common divisor of $a$ and $b.$ Then $d$ is the [[Greatest Common Divisor (GCD)|GCD]] of $a$ and $b$ iff $\gcd\left( \frac{a}{d}, \frac{b}{d} \right)=1$: that is $a/d$ and $b/d$ are [[Coprime Integers|coprime]]. **Proof**: ...