# Perfect Numbers

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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.

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