Euclidean Algorithm/Examples/119 and 272/Proof
< Euclidean Algorithm | Examples | 119 and 272
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Examples of Use of Euclidean Algorithm
The GCD of $119$ and $272$ is found to be:
- $\gcd \set {119, 272} = 17$
Proof
\(\text {(1)}: \quad\) | \(\ds 272\) | \(=\) | \(\ds 2 \times 119 + 34\) | |||||||||||
\(\text {(2)}: \quad\) | \(\ds 119\) | \(=\) | \(\ds 3 \times 34 + 17\) | |||||||||||
\(\text {(3)}: \quad\) | \(\ds 34\) | \(=\) | \(\ds 2 \times 17\) |
Thus:
- $\gcd \set {119, 272} = 17$
$\blacksquare$