GCD from Prime Decomposition/Examples/2187 and 999
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Example of Use of GCD from Prime Decomposition
The greatest common divisor of $2187$ and $999$ is:
- $\gcd \set {2187, 999} = 27$
Proof
| \(\ds 2187\) | \(=\) | \(\ds 3^7\) | ||||||||||||
| \(\ds 999\) | \(=\) | \(\ds 3^3 \times 37\) | ||||||||||||
| \(\ds \leadsto \ \ \) | \(\ds 2187\) | \(=\) | \(\ds 3^7 \times 37^0\) | |||||||||||
| \(\ds 999\) | \(=\) | \(\ds 3^3 \times 37^1\) | ||||||||||||
| \(\ds \leadsto \ \ \) | \(\ds \gcd \set {2187, 999}\) | \(=\) | \(\ds 3^3 \times 37^0\) | |||||||||||
| \(\ds \) | \(=\) | \(\ds 27\) |
$\blacksquare$
Sources
- 1971: George E. Andrews: Number Theory ... (previous) ... (next): $\text {2-4}$ The Fundamental Theorem of Arithmetic: Exercise $6 \ \text{(d)}$