Euclidean Algorithm 
Example 4
\(z=-1+4\sqrt{2}\;\;\;\;\;\;\;\;\;\; w=\sqrt{2}\)
\(\begin{array}{rcl}
-1+4\sqrt{2} & = & \sqrt{2}\left(3-\sqrt{2}\right)+1+\sqrt{2}\\
\sqrt{2} & = & \left(1+\sqrt{2}\right)\left(2-\sqrt{2}\right)
\end{array}\)
\(gcd\left(-1+4\sqrt{2},\sqrt{2}\right)=1+\sqrt{2}\)
