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To find the greatest common divisor of two large numbers, repeatedly apply the division-with-remainder step. Start by dividing the larger number by the smaller number.

Conditions: The inputs are two positive integers.; The division algorithm is applied at each step.; The process stops when a remainder equals 0.

To find the greatest common divisor of two large numbers, repeatedly apply the division-with-remainder step. Start by dividing the larger number by the smaller number.

Conditions: The inputs are two positive integers.; The division algorithm is applied at each step.; The process stops when a remainder equals 0.

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.

To compute $\gcd(5295, 4321)$, apply the Euclidean algorithm by repeatedly dividing the previous divisor by the previous remainder. Start with $5295 = 1 \cdot 4321 + 974$.

Conditions: The inputs are 5295 and 4321.; The Euclidean algorithm is used.; The division algorithm is applied at each step.

To compute $\gcd(5295, 4321)$, apply the Euclidean algorithm by repeatedly dividing the previous divisor by the previous remainder. Start with $5295 = 1 \cdot 4321 + 974$.

Conditions: The inputs are 5295 and 4321.; The Euclidean algorithm is used.; The division algorithm is applied at each step.

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.