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.

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