An abundant number or excessive number is a number for which the sum of its proper divisors is greater than the number itself.

An abundant number is a number n for which the sum of divisors σ(n)>2n, or, equivalently, the sum of proper divisors (or aliquot sum) s(n)>n.

Example: 48 is a abundant number.

1 and 48

2 and 24

3 and 16

4 and 12

6 and 8

If we leave out the number we started with, 48, and add all the other factors, we get 76.

1 + 2 + 3 + 4 + 6 + 8 + 12 + 16 + 24 = 76

Hence this, 48 is a Abundant Number

Other Abundant Numbers

12, 18, 20, 24, 30, 36, 40, 42, 48, 54, 56, 60, 66, 70, 72, 78, 80, 84, 88, 90, 96, 100, 102, 104, 108, 112, 114, 120…etc..