What would you like to understand?

The base case for the Euclidean algorithm is when the second argument of the pair is zero. At this point, the algorithm stops, and the first argument is returned as the greatest common divisor.

Conditions: The algorithm is in the process of replacing pairs using $\gcd(a,b)=\gcd(b,a\bmod b)$.; The second argument $b$ has reached zero.

The base case for the Euclidean algorithm is when the second argument of the pair is zero. At this point, the algorithm stops, and the first argument is returned as the greatest common divisor.

Conditions: The algorithm is in the process of replacing pairs using $\gcd(a,b)=\gcd(b,a\bmod b)$.; The second argument $b$ has reached zero.

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 $\gcd(a,b)=\gcd(b,a\bmod b)$.