Euclidean Algorithm/Examples/341 and 527

Examples of Use of Euclidean Algorithm

The GCD of $341$ and $527$ is found to be:

$\gcd \set {341, 527} = 31$

Integer Combination

$31$ can be expressed as an integer combination of $341$ and $527$:

$31 = 2 \times 527 - 3 \times 341$

Proof

\(\text {(1)}: \quad\)

\(\ds 527\)

\(=\)

\(\ds 1 \times 341 + 186\)

\(\text {(2)}: \quad\)

\(\ds 341\)

\(=\)

\(\ds 1 \times 186 + 155\)

\(\text {(3)}: \quad\)

\(\ds 186\)

\(=\)

\(\ds 1 \times 155 + 31\)

\(\ds 155\)

\(=\)

\(\ds 5 \times 31\)

Sources

• 1971: George E. Andrews: Number Theory ... (previous) ... (next): $\text {2-2}$ Divisibility: Example $\text {2-7}$