Euclidean Algorithm/Examples/56 and 72/Proof

Examples of Use of Euclidean Algorithm

The GCD of $56$ and $72$ is found to be:

$\gcd \set {56, 72} = 8$


Proof

\(\text {(1)}: \quad\) \(\ds 72\) \(=\) \(\ds 1 \times 56 + 16\)
\(\text {(2)}: \quad\) \(\ds 56\) \(=\) \(\ds 3 \times 16 + 8\)
\(\text {(3)}: \quad\) \(\ds 16\) \(=\) \(\ds 2 \times 8\)


Thus:

$\gcd \set {56, 72} = 8$

$\blacksquare$

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.