> [!NOTE] Definition (Greatest Common Divisor) > Let $(D,+,\times)$ be an [[Integral Domain|integral domain]]. Let $D[x]$ be the [[Ring of Polynomial Forms|ring of polynomial forms]] over $D$ in $x$ ([[Ring of Polynomial Forms over Integral Domain is Integral Domain|which is an integral domain]]). Let $f,g\in D[x].$ Then $d$ is a greatest common divisor of $f$ and $g$ iff $d$ is a [[Divisibility in Ring of Polynomial Forms|divisor]] of both $f$ and $g$ and any other common divisor divides $d.$ # Properties Note that if $D$ is a field then we [[Bézout's Identity for Ring of Polynomial Forms Over Field]] since $D[x]$ will be a Euclidean domain.