Understanding Armstrong Numbers: Definition, Examples, and How to Identify Them
A positive integer is called an Armstrong number (of order n) if
abcd... = an + bn + cn + dn +In the case of an Armstrong number of 3 digits, the sum of cubes of each digit is equal to the number itself. For example, 153 is an Armstrong number because
153 = = 13 + 53 + 33 = 1*1*1 + 5*5*5 + 3*3*3Complete step by step solution:
An Armstrong number is defined as the sum of nth power of each digit to a n digit number is equal to that number.
Let N = abc is a three number which is an Armstrong number, so the mathematical form of the number is N = a3 + b3 + c3 .
if N = abcd be a four digit number then we have N = a4 + b4 + c4 + d4 , similarly for five, six, seven and so on… Let us explain the definition using the example.
Example: 1
Suppose we take a number N=153 which is three-digit number,
Now we calculate
13 + 53 + 33 = 1 + 125 + 27 = 153
So, we can write
153 = 13 + 53 + 33
Hence, we can say that 153 is an Armstrong number.
Example: 2
Take another number of four digit N=1634
Now here we calculate
14 + 64 + 34 + 44 = 1 + 1296 + 81 + 256 = 1634
So, we can write
1634 = 14 + 64 + 34 + 44
Hence, we can say that the number 1634 is also an Armstrong number.
So, the above illustration explains the definition of Armstrong number.
Note: it should be noted that this number is also known as a Narcissistic number as well as plus perfect number. As per the definition all one-digit numbers are Armstrong numbers. There are no any two digits Armstrong numbers. Three-digit Armstrong numbers are 153, 370, 371 and 407.