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Age 11 to 14 Short
Challenge Level

Given any positive integer $n$, Paul adds together the distinct factors of $n$, other than $n$ itself.

Which of the numbers $1$, $3$, $5$, $7$ and $9$ can never be Paul's answer?

If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.

This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.