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Smallest Abundant Number

Age 11 to 14 Short
Challenge Level


An abundant number is a positive integer $N$ such that the sum of the factors of $N$ (not including $N$ itself) is greater than $N$.

What is the smallest abundant number?


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.
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.
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