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Smallest Abundant Number

Age 11 to 14 Short
Challenge Level

Answer: 12

Primes - only factor is 1 (and self) so not abundant

number factors sum abundant?
4 1,2 3 No
6 1,2,3 6 No
8 1,2,4 7 No
9 1,3 4 No
10 1,2,5 7 No
12 1,2,3,4,6 16 Yes

This shows that the smallest abundant number is $12$.

$6$ is called a perfect number, as the sum of its factors is equal to the number.


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