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GCD is simply a mathematical operator. You can define any operator on one or more inputs. That is their definition - they do not require justification.
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What is the gcd of 125 and 225?
GCD(125, 225) = 25 GCD(125, 225) = 25 GCD(125, 225) = 25 GCD(125, 225) = 25
What is Euclid's Algorithm?
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