Euclidean Domain/Euclidean Algorithm/Examples

Examples of Use of Euclidean Algorithm in Euclidean Domain

GCD of $5 i$ and $3 + i$ in Ring of Gaussian Integers

The GCD of $5 i$ and $3 + 1$ in the ring of Gaussian integers is found to be:

$\gcd \set {5 i, 3 + 1} = 1 + 2 i$

and its associates $-1 - 2 i$, $-2 + i$ and $2 - i$.