What is the GCD of 8463 and 1001?
By performing the Euclidean divisions, we obtain:

$$
\begin{gathered}
8463=8 \times 1001+455 \\
1001=2 \times 455+91 \\
455=5 \times 91+0
\end{gathered}
$$

The GCD is the last non-zero remainder, which is: 91. We can trace back the Euclidean algorithm above to find the Bézout relation: $91=1001-2 \times 455=1001-2 \times(8463-8 \times 1001)=$ $17 \times 1001-2 \times 8463$.