Euclidean Algorithm/Examples/306 and 657

Examples of Use of Euclidean Algorithm

The GCD of $306$ and $657$ is:

$\gcd \set {306, 657} = 9$

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

$\ds 657$

$=$

$\ds 2 \times 306 + 45$

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

$\ds 306$

$=$

$\ds 6 \times 45 + 36$

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

$\ds 45$

$=$

$\ds 1 \times 36 + 9$

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

$\ds 36$

$=$

$\ds 4 \times 9$

Thus:

$\gcd \set {306, 657} = 9$

$\blacksquare$

1980: David M. Burton: Elementary Number Theory (revised ed.) ... (previous) ... (next): Chapter $2$: Divisibility Theory in the Integers: $2.3$ The Euclidean Algorithm: Problems $2.3$: $1$