4.3 Perfect, deficient and abundant numbers
When we decide if a number is perfect, deficient or abundant, we look at the sum of numbers a specific numbers is divisible by. If all the numbers, except the number itself is added then we can decide if the number is deficient, abundant or perfect.
Perfect Numbers
For a number to be perfect, the sum of its divisors, except for the number itself, should be equal to that specific number.
Example
We can look at 28.
28
1 
= 
28 
28
2 
= 
14 
28
4 
= 
7 
28
7 
= 
4 
28
14 
= 
2 
28
28 
= 
1 
The number 28 has 6 divisors, namely 1, 2, 4, 7, 14 and 28. Without using 28 itself, the sum of the other divisors is added.
1 + 2 + 4 + 7 + 14 = 28
28 is then considered a perfect number.

Deficient Numbers
A deficient numbers is larger than the sumer of its divisor, except the number itself.
Example
We can look at the number 14.
14
1 
= 
14 
14
2 
= 
7 
14
7 
= 
2 
14
14 
= 
1 
The number 14 has 4 divisors, namely 1, 2, 7 and 14. The number 14 should not be included in the sum, so we get:
1 + 2 + 7 = 10
Because 10 is less than 14, we can conclude that 14 is a deficient number.
Abundant Numbers
An abundant numbers is less than the sum of its divisors.
Example
We can try the number 18.
18
1 
= 
18 
18
2 
= 
9 
18
3 
= 
6 
18
6 
= 
3 
18
9 
= 
2 
18
18 
= 
1 
The number 18 has 6 divisors, namely 1, 2, 3, 6, 9 and 18. 18 should not included in the sum and we get:
1 + 2 + 3 + 6 + 9 = 21
Because 21 is larger than 18, we can conclude that 18 is an abundant number. 