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Just wondering when using the Euclidean Algorithm to find gcd of 4+7i and 1+3i. Where does 2 and 2+i come from in the follwoing?

4+7i = 2*(1+3i)+(2+i)

1+3i=(1+i)*(2+i) +0?

I know you didvide them to get (5-i)/2 and then take closest Gaussian integer then not sure where to go.