Euclidean Algorithm/Examples/361 and 1178

Examples of Use of Euclidean Algorithm

The GCD of $361$ and $1178$ is:

$\gcd \set {361, 1178} = 19$

$\text {(1)}: \quad$

$\ds 1178$

$=$

$\ds 3 \times 361 + 95$

$\text {(2)}: \quad$

$\ds 361$

$=$

$\ds 3 \times 95 + 76$

$\text {(3)}: \quad$

$\ds 95$

$=$

$\ds 1 \times 76 + 19$

$\text {(4)}: \quad$

$\ds 76$

$=$

$\ds 4 \times 19$

Thus:

$\gcd \set {361, 1178} = 19$

$\blacksquare$

1971: George E. Andrews: Number Theory ... (previous) ... (next): $\text {2-2}$ Divisibility: Exercise $1 \ \text{(b)}$