Competition problem — Number theory

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Number theory Difficulty 3.8 AMC 10/12 Find the answer South Africa

One of the factors of $48$ is chosen at random. What is the probability that the chosen factor is NOT a multiple of $4$ ?

Pick one

Solution

There are ten factors: $1$ , $2$ , $3$ , $4$ , $6$ , $8$ , $12$ , $16$ , $24$ , $48$ . Four of them are not multiples of $4$ , viz. $1$ , $2$ , $3$ , $6$ . The probability is therefore $\frac{4}{10}$ or $40\%$ .

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