Exercise 1648Number theory › Divisibility and gcdOlympiadAdded 3 Nov 2026

An application of the Euclidean algorithm

#Euclidean algorithm#expansion#continued fraction

Statement

Use the Euclidean algorithm to find the continued fraction expansion of $1071/462$ .

Hint

Each quotient in the algorithm gives a coefficient in the continued fraction.

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Euclidean. $1071=2\cdot462+147$ , $462=3\cdot147+21$ , $147=7\cdot21+0$ .

Quotients. $2,3,7$ .

Continued fraction. $1071/462=2+\frac{1}{3+\frac{1}{7}}$ .

Conclusion. The continued fraction expansion of $1071/462$ is $[2;3,7]$ .