Euclidean Algorithm/Algorithmic Nature

Algorithm
It can be seen from the definition that the Euclidean Algorithm is indeed an algorithm:


 * Finiteness: As has been seen, the algorithm always terminates after a finite number of steps.
 * Definiteness: Each of the steps is precisely defined.
 * The inputs are $a$ and $b$.
 * The output is $\gcd \left\{{a, b}\right\}$.
 * Effectiveness: Each operation is finite in extent and can be effectively performed.