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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