Math

What are perfect Numbers ?

Perfect Numbers


A perfect number is defined as a number which is equal to the sum of its positive factors.

 

Let’s take an example –

The first perfect number (integer) is 6.

A factor of 6 are – 1, 2, 3.

Sum of 1, 2, 3, – 1+2+3 = 6.

Therefore, 6 is a perfect number.

In order to find the perfect number, the number itself should not be included in the list of factors.

 

Let’s take a few more examples:-

  • N=28

Factors of 28 = 1, 2, 4, 7, 14

Sum = 1+2+4+7+14 =28

  • N=496

Factors of 496 =1, 2, 4, 8, 16, 31, 62, 124, 248

Sum= 1+2+4+8+16+31+62+124+248 = 496

 

First, five perfect numbers are –

6, 28, 496, 8128, 33550336

We know that (2^k – 1) is a form of a prime number, then 2^(k-1)(2^k – 1) is a form of the perfect number.

Where k must be a prime number.

We can write :-

6 = 2^1(2^2 – 1)

28 = 2^2(2^3 – 1)

 

Magic of perfect numbers can be seen in our nature also.

Moons period is of 28 days.

About the author

Mayuri Bhoyar

Leave a Comment