Euclidean Algorithm/Examples/24 and 138/Proof

Examples of Use of Euclidean Algorithm

The GCD of $24$ and $138$ is found to be:

$\gcd \set {24, 138} = 6$


Proof

\(\text {(1)}: \quad\) \(\ds 138\) \(=\) \(\ds 5 \times 24 + 18\)
\(\text {(2)}: \quad\) \(\ds 24\) \(=\) \(\ds 1 \times 18 + 6\)
\(\text {(3)}: \quad\) \(\ds 18\) \(=\) \(\ds 3 \times 6\)


Thus:

$\gcd \set {24, 138} = 6$

$\blacksquare$

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