Competition problem — Number theory

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Number theory Difficulty 5.5 AIME, harder Find the answer

Example 9 Convert 117 to an octal number equals what?

Convert the above text into English, please retain the original text's line breaks and format, and output the translation result directly.

Solution

Solve: From $\frac{117}{8}=14+\frac{5}{8}$ we get $b_{0}=5$ , from $\frac{14}{8}=1+\frac{6}{8}$ we get $b_{1}=6, b_{2}=1$ ,
that is
$117=(165)_{8}$

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.