# Euclidean Algorithm/Examples/341 and 527/Proof

## Examples of Use of Euclidean Algorithm

The GCD of $341$ and $527$ is found to be:

$\gcd \set {341, 527} = 31$

## Proof

 $\text {(1)}: \quad$ $\ds 527$ $=$ $\ds 1 \times 341 + 186$ $\text {(2)}: \quad$ $\ds 341$ $=$ $\ds 1 \times 186 + 155$ $\text {(3)}: \quad$ $\ds 186$ $=$ $\ds 1 \times 155 + 31$ $\ds 155$ $=$ $\ds 5 \times 31$

Thus:

$\gcd \set {341, 527} = 31$

$\blacksquare$