# Perfect Numbers

A perfect number is a positive integer that is equal to the sum of its proper divisors (factors), excluding the number itself.

Learn about factors.

Explore the different types of numbers.

Given below is a flowchart to determine whether or not a given number is PERFECT.

## Solved Examples

### Example 1:

Check whether \(28\) is a perfect number or not.

**Step 1:**

List all the factors of \(28\) other than 28 itself.

Factors of \(28 = \{ 1, 2, 4, 7, 14\}\)

**Step 2:**

Calculate the sum of factors.

\(\begin{align}\text{Sum of Factors} &= 1 + 2 + 4 + 7 + 14\\ &= 28 \end{align}\)

**Step 3:**

Check whether the Sum of Factors is equal to the number itself.

Sum of Factors \(= 28\)

Number \(= 28\)

Thus, \(28\) is a **perfect number**.

### Example 2:

Check whether \(33\) is a perfect number or not.

**Step 1:**

List all the factors of \(33\) other than \(33\) itself.

\(\begin{align} \text{Factors of }33 = \{1, 3, 11\} \end{align}\)

**Step 2:**

Calculate the sum of factors.

\(\begin{align} \text{Sum of Factors}& = 1 + 3 + 11\\&= 15 \end{align}\)

**Step 3:**

Check whether the Sum of Factors is equal to the number itself.

Sum of Factors \(= 15\)

Number \(= 33\)

Thus, \(33\) is a NOT **perfect number**.

## Practice Questions

1) Check whether \(496\) is a perfect number or not.

2) Check whether \(394\) is a perfect number or not.