Competition problem — Number theory

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Number theory Difficulty 3.7 AMC 10/12 Find the answer South Africa

If $\frac{12}{x}$ is a natural number and $x$ is a natural number, how many possible values are there for $x$ ?

Pick one

Solution

$x$ must be a divisor of $12$ , and the possibilities are $1$ , $2$ , $3$ , $4$ , $6$ , $12$ , which is $6$ in all.

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Source: MathNet, licensed CC-BY-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.