# What is an Abundant Number?

## What is an Abundant Number?

An Abundant Number is a positive integer for which the sum of all its Proper divisors (factors) is more than the original number.

Abundant number is  also called Excessive Numbers.

## Examples of Abundant Numbers

Let us understand Abundant Number with a few examples.

Example 1.  20 is an Abundant number.

Proper divisors of 20 = 1, 2, 4, 5, and 10.

Sum = 1 + 2 + 4 + 5 + 10 = 22

As 22 > 20,

Therefore, 20 is an Abundant number or an Excessive number.

Example 2.  114 is an Abundant number.

Proper divisors of 114 = 1, 2, 3, 6, 19, 38, and 57.

Sum – 1 + 2 + 3 + 6 + 19 + 38 + 57 = 126

As 126 > 114,

Therefore, 114 is an Abundant number.

There are infinitely many Abundant numbers.

## Properties of Abundant numbers

1. No Prime Number is an Abundant number.

2. All the multiples of Abundant numbers are also Abundant numbers.

3. Every proper multiple of a perfect number is an Abundant number.

4. Every integer greater than 20161 can be written as the sum of two abundant numbers.

## Abundant Numbers’ list

The first 28 abundant numbers are:

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,….

Chapter-wise Quiz/MCQ/Test:

Chapter-wise Quiz/MCQ/Test:
Sample Papers:

Board Papers

CBSE Class 10 Previous years’ Board Papers