Euclidean Algorithm/Examples/132 and 473

Examples of Use of Euclidean Algorithm

The GCD of $132$ and $473$ is:

$\gcd \set {132, 473} = 11$

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

$\ds 473$

$=$

$\ds 3 \times 132 + 77$

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

$\ds 132$

$=$

$\ds 1 \times 77 + 55$

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

$\ds 77$

$=$

$\ds 1 \times 55 + 22$

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

$\ds 55$

$=$

$\ds 2 \times 22 + 11$

$\text {(5)}: \quad$

$\ds 22$

$=$

$\ds 2 \times 11$

Thus:

$\gcd \set {132, 473} = 11$

$\blacksquare$

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