Armstrong number

Armstrong number

Let's see a magic!!!

The sum of  cubes of digits of 153 is 153 itself!

 

 Yes! It's very interesting.
These types of numbers are known as Armstrong number.

Definition:

    A number with n digits is called an Armstrong number if the sum of n-th powers of its all digits be the same number.

  i.e., for a three digit number the sum of cubes of its all digits must be equal with the original number. for a number with four digits the original number  must be equals to the sum of  fourth power of all its digits. And so on.

some examples are follows:

0,1,2,3,4,5,6,7,8,9,153,370,371,407,1634,...

  Interesting fact about an Armstrong  number with n digits is as mentioned in the definition is that , the sum of the  n-th power of the digits (for all  the  digits )is equals to the original number.
  How to check a number is Armstrong number or not:
   (1) First, find the number of digits of the given number (say, n).
   (2) Then, calculate the n-th powers  of  the all digits.
    (3) sum all the results.
     (4) Now, if the sum is equals to the original number ,then the original number is a armstrong number; otherwise it is not an armstrong number.

 Check 153 is an armstrong number or not:
  (1) The number of digits of 153 is 3.
  (2) The cubes of 1,5and 3 are 1, 125 and 27 respectively.
   (3) now sum of 1,125 and 27 is 153.
  (4) so, the sum 153 is equals to the original number 153. Thus 153 is an armstrong number.
 
   Check 121 is  an armstrong numbers or not:
  (1) The number of digits of 121 is 3.
  (2) The cubes of 1,2and1 are 1,4 and 1 respectively.
   (3) now the sum of 1, 4 and 1 is 6.
   (4) so, the sum 6 is not equals to the original number 121. Thus, 121 is not a armstrong number.

It is to be noted that, an Armstrong number is also known as narcissistic number or a plus perfect number.

 If you find out any incorrect information or know anything more about this , please write it in the comment section!