What would you like to understand?

The Euclidean algorithm keeps the GCD by repeatedly applying the step $\gcd(a,b)=\gcd(b,a\bmod b)$ for nonnegative $a$ and positive $b$. This replaces the pair with the divisor and the remainder, preserving the greatest common divisor.

Conditions: $a$ is a nonnegative integer.; $b$ is a positive integer.; The operation $a\bmod b$ computes the remainder of $a$ divided by $b$.

The Euclidean algorithm keeps the GCD by repeatedly applying the step $\gcd(a,b)=\gcd(b,a\bmod b)$ for nonnegative $a$ and positive $b$. This replaces the pair with the divisor and the remainder, preserving the greatest common divisor.

Conditions: $a$ is a nonnegative integer.; $b$ is a positive integer.; The operation $a\bmod b$ computes the remainder of $a$ divided by $b$.

To trace the Euclidean algorithm for $\gcd(10,15)$, repeatedly apply the step $\gcd(a,b)=\gcd(b,a\bmod b)$ until the second argument is zero. The sequence is $\gcd(10,15)=\gcd(15,10)=\gcd(10,5)=\gcd(5,0)=5$.

Conditions: The initial pair is (10, 15).; The algorithm uses the Euclidean step $\gcd(a,b)=\gcd(b,a\bmod b)$.; The process stops when the second argument is zero.

To trace the Euclidean algorithm for $\gcd(10,15)$, repeatedly apply the step $\gcd(a,b)=\gcd(b,a\bmod b)$ until the second argument is zero. The sequence is $\gcd(10,15)=\gcd(15,10)=\gcd(10,5)=\gcd(5,0)=5$.

Conditions: The initial pair is (10, 15).; The algorithm uses the Euclidean step $\gcd(a,b)=\gcd(b,a\bmod b)$.; The process stops when the second argument is zero.