GCD with the Euclidean algorithm

Statement

Compute $\gcd(1071,462)$ using the Euclidean algorithm.

Solution

Perform successive divisions, keeping each remainder: $\begin{aligned} 1071 &= 2\cdot 462 + 147, \ 462 &= 3\cdot 147 + 21, \ 147 &= 7\cdot 21 + 0. \end{aligned}$ The last non-zero remainder is the GCD: $\gcd(1071,462) = \boxed{21}.$