# The Euclidean Algorithm

Here: Complexity of Euclidean Algorithm we prove that if $$a,b\in\mathbb{Z},a>b>0$$, then the number of steps in the Euclidean algorithm is about $$\log_{10}\left(b\right)/\log_{10}\left(\Phi\right)$$; which is at most five times the number of decimal digits of $$b$$.

There are more efficient algorithms to find the greatest common divisor between two numbers, indeed. This is nothing but a starting point.