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Answer: 12
Primes - only factor is 1 (and self) so not abundant
Smallest Abundant Number
Age 11 to 14
ShortChallenge 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.
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