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, 2006

Number theory Difficulty 2.0 Junior Find the answer Canada

A positive integer is called multiplicatively perfect if it is equal to the product of its proper divisors. For example, $10$ is multiplicatively perfect since its proper divisors are $1$ , $2$ and $5$ , and it is true that $1 \times 2 \times 5 = 10$ . How many multiplicatively perfect integers are there between $2$ and $30$ ?

(A) $9$ (B) $5$ (C) $8$ (D) $6$ (E) $4$

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Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.