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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.

When the Euclidean algorithm yields a greatest common divisor of 1, it means the two input numbers are relatively prime (or coprime). This indicates that they share no common positive integer divisors other than 1.

Conditions: The inputs are natural numbers.; The Euclidean algorithm terminates with a last nonzero remainder of 1.

When the Euclidean algorithm yields a greatest common divisor of 1, it means the two input numbers are relatively prime (or coprime). This indicates that they share no common positive integer divisors other than 1.

Conditions: The inputs are natural numbers.; The Euclidean algorithm terminates with a last nonzero remainder of 1.

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.