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The Euclidean algorithm using division terminates when one of the entries in the current pair $(a,b)$ becomes zero. Specifically, when the remainder $r$ in the step $b=aq+r$ becomes zero, the next pair is $(0,a)$ or $(a,0)$, and the algorithm stops, returning the non-zero entry as the gcd.

Conditions: The algorithm uses the step $\gcd(a,b) = \gcd(b, a \bmod b)$.; $a$ and $b$ are nonnegative integers.; Termination occurs when the second argument is 0.

The Euclidean algorithm using division terminates when one of the entries in the current pair $(a,b)$ becomes zero. Specifically, when the remainder $r$ in the step $b=aq+r$ becomes zero, the next pair is $(0,a)$ or $(a,0)$, and the algorithm stops, returning the non-zero entry as the gcd.

Conditions: The algorithm uses the step $\gcd(a,b) = \gcd(b, a \bmod b)$.; $a$ and $b$ are nonnegative integers.; Termination occurs when the second argument is 0.

You should stop the Euclidean algorithm when the second argument of the pair becomes zero. At this point, the first argument is the greatest common divisor.

Conditions: The algorithm is tracing the steps of the Euclidean algorithm.; The pair is represented as $(a,b)$.; The operation is $\gcd(a,b)=\gcd(b,a\bmod b)$.

You should stop the Euclidean algorithm when the second argument of the pair becomes zero. At this point, the first argument is the greatest common divisor.

Conditions: The algorithm is tracing the steps of the Euclidean algorithm.; The pair is represented as $(a,b)$.; The operation is $\gcd(a,b)=\gcd(b,a\bmod b)$.