You may also like

Consecutive Numbers

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

Calendar Capers

Choose any three by three square of dates on a calendar page...

Days and Dates

Investigate how you can work out what day of the week your birthday will be on next year, and the year after...

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.