# Euclidean Algorithm/Algorithmic Nature

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## 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.