Narcissistic Number

Narcissistic number is a number that returns the original number when each digit is raised separately to the power of the number of digits.

Checking a Narcissistic Number

Step 1: Consider any number.

Step 2: (Number)^{power of the number of digits}

If the number obtained in Step 2 is same as the number considered in Step 1, it is a Narcissistic number. But if the number obtained in Step 2 is different than the number considered in Step 1, it is not a Narcissistic number.

Examples

Example 1

Step 1: Consider number 0.

Step 2: 0¹ => 0.

The number obtained in Step 2 is same as the number considered in Step 1. Therefore, 0 is a Narcissistic number.

Example 2

Step 1: Consider number 1.

Step 2: 1¹ => 1.

The number obtained in Step 2 is same as the number considered in Step 1. Therefore, 1 is a Narcissistic number.

Example 3

Step 1: Consider number 2.

Step 2: 2¹ => 2.

The number obtained in Step 2 is same as the number considered in Step 1. Therefore, 2 is a Narcissistic number.

Example 4

Step 1: Consider number 3.

Step 2: 3¹ => 3.

The number obtained in Step 2 is same as the number considered in Step 1. Therefore, 3 is a Narcissistic number.

Example 5

Step 1: Consider number 4.

Step 2: 4¹ => 4.

The number obtained in Step 2 is same as the number considered in Step 1. Therefore, 4 is a Narcissistic number.

Example 6

Step 1: Consider number 5.

Step 2: 5¹ => 5.

The number obtained in Step 2 is same as the number considered in Step 1. Therefore, 5 is a Narcissistic number.

Example 7

Step 1: Consider number 6.

Step 2: 6¹ => 6.

The number obtained in Step 2 is same as the number considered in Step 1. Therefore, 6 is a Narcissistic number.

Example 8

Step 1: Consider number 7.

Step 2: 7¹ => 7.

The number obtained in Step 2 is same as the number considered in Step 1. Therefore, 7 is a Narcissistic number.

Example 9

Step 1: Consider number 8.

Step 2: 8¹ => 8.

The number obtained in Step 2 is same as the number considered in Step 1. Therefore, 8 is a Narcissistic number.

Example 10

Step 1: Consider number 9.

Step 2: 9¹ => 9.

The number obtained in Step 2 is same as the number considered in Step 1. Therefore, 9 is a Narcissistic number.

Example 11

Step 1: Consider number 10.

Step 2: 1² + 0² => 1 x 1 + 0 x 0 => 1 + 0 => 1.

The number obtained in Step 2 is different than the number considered in Step 1. Therefore, 10 is not a Narcissistic number.

Hope you have understood this amazing concept of the Narcissistic number. To check whether a number is a Narcissistic number or not, use the above examples. In case of any query, please feel free to provide your valuable comments.