What would you like to understand?

The Euclidean algorithm computes the greatest common divisor by repeatedly applying the division algorithm. Starting with two natural numbers $a$ and $b$, you divide the larger by the smaller to get a quotient and a remainder.

Conditions: The inputs $a$ and $b$ are natural numbers.; The division algorithm is applied repeatedly.; The process stops when a remainder equals 0.

The Euclidean algorithm computes the greatest common divisor by repeatedly applying the division algorithm. Starting with two natural numbers $a$ and $b$, you divide the larger by the smaller to get a quotient and a remainder.

Conditions: The inputs $a$ and $b$ are natural numbers.; The division algorithm is applied repeatedly.; The process stops when a remainder equals 0.

To form the next division line, you take the divisor from the previous line and make it the dividend of the new line. Then, you take the remainder from the previous line and make it the divisor of the new line.

Conditions: You have just completed a division step in the Euclidean algorithm.; The previous remainder is not 0.

To form the next division line, you take the divisor from the previous line and make it the dividend of the new line. Then, you take the remainder from the previous line and make it the divisor of the new line.

Conditions: You have just completed a division step in the Euclidean algorithm.; The previous remainder is not 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.

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.