Question: How does the validity of this method of finding gcds depend on the Fundamental Theorem of Arithmetic? 1464463 72 X 112 X 13 X 19

How does the validity of this method of finding gcds depend on the Fundamental Theorem of Arithmetic?

1464463 72 X 112 X 13 X 19 14108963 112 X 17 X 193 so gcd(1464463, 14108963) = 112 X 19 = 2299.

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