Euclidean Algorithm/Examples/52 and 273

Examples of Use of Euclidean Algorithm

The GCD of $52$ and $273$ is found to be:

$\gcd \set {52, 273} = 13$


Proof

\(\text {(1)}: \quad\) \(\ds 273\) \(=\) \(\ds 5 \times 52 + 13\)
\(\text {(2)}: \quad\) \(\ds 52\) \(=\) \(\ds 4 \times 13\)


Thus:

$\gcd \set {52, 273} = 13$

$\blacksquare$


Sources

  • 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Euclidean algorithm
  • 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Euclidean algorithm
This article is issued from ProofWiki. The text is available under Creative Commons Attribution-ShareAlike License unless otherwise noted. Additional terms may apply for the media files.