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Answers for “为什么最后一个非零余数 $r_n$ 是 $\gcd(a,b)$?”

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The Euclidean algorithm computes the greatest common divisor by repeatedly applying the division algorithm. Starting with two natural numbers aa and bb, you divide the larger by the smaller to get a quotient and a remainder.

Conditions: The inputs aa and bb are natural numbers.; The division algorithm is applied repeatedly.; The process stops when a remainder equals 0.