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Strictly speaking, the standard stopping condition for the Euclidean algorithm is to continue until the remainder is 0. The last nonzero remainder is then the gcd.

Conditions: The inputs are natural numbers.; The Euclidean algorithm is being applied.

Strictly speaking, the standard stopping condition for the Euclidean algorithm is to continue until the remainder is 0. The last nonzero remainder is then the gcd.

Conditions: The inputs are natural numbers.; The Euclidean algorithm is being applied.

In the displayed Euclidean algorithm, $a$ and $b$ are the two initial natural numbers whose gcd is being found. $q_i$ represents the quotient at the $i$-th division step.

Conditions: The symbols are from the general statement of the Euclidean algorithm on the left board.

In the displayed Euclidean algorithm, $a$ and $b$ are the two initial natural numbers whose gcd is being found. $q_i$ represents the quotient at the $i$-th division step.

Conditions: The symbols are from the general statement of the Euclidean algorithm on the left board.

The Euclidean algorithm is a method for finding the greatest common divisor (gcd) of two natural numbers. It is set up by repeatedly applying the division algorithm.

Conditions: The inputs $a$ and $b$ are natural numbers.; The division algorithm is used at each step.

The Euclidean algorithm is a method for finding the greatest common divisor (gcd) of two natural numbers. It is set up by repeatedly applying the division algorithm.

Conditions: The inputs $a$ and $b$ are natural numbers.; The division algorithm is used at each step.