Euclidean Algorithm/Algorithmic Nature

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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.