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Number theory Difficulty 2.5 Junior Find the answer Canada

When two positive integers $p$ and $q$ are multiplied together, their product is 75. The sum of all of the possible values of $p$ is

Pick one

Solution

Since $75 = 3 \times 5 \times 5$ , we can factor 75 in three different ways: $75 = 1\times 75 = 3 \times 25 = 5 \times 15$ If $pq = 75$ with $p$ and $q$ integers, then the possible values of $p$ are thus $1,3,5,15,25,75$ .

The sum of these values is $1+3+5+15+25+75=124$ .

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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.