Euclidean Algorithm/Examples/108 and 243

Examples of Use of Euclidean Algorithm

The GCD of $108$ and $243$ is:

$\gcd \set {108, 243} = 27$


Proof

\(\text {(1)}: \quad\) \(\ds 243\) \(=\) \(\ds 2 \times 108 + 27\)
\(\text {(2)}: \quad\) \(\ds 108\) \(=\) \(\ds 4 \times 27\)

Thus:

$\gcd \set {108, 243} = 27$

$\blacksquare$


Sources

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