# Armstrong number in C – Complete guide with example

Armstrong numbers are an interesting concept in mathematics and programming. They are frequently used in coding interviews and as exercises for programmers to test their skills. In this blog post, we will dive deep into the concept of Armstrong numbers, discuss their properties, and learn how to implement a program to find Armstrong numbers in the C programming language. This guide is designed for beginner to intermediate developers, and we will provide detailed explanations and code examples to help you grasp the concepts easily.

## What is an Armstrong Number?

An Armstrong number (also known as a pluperfect number, narcissistic number, or pluperfect digital invariant) is a number that is equal to the sum of its own digits, each raised to the power of the number of digits in the number. In other words, a number `n`

is an Armstrong number if the sum of its digits, each raised to the `n-th`

power, is equal to the number itself.

For example, the number 153 is an Armstrong number because 1^3 + 5^3 + 3^3 = 153.

## Properties of Armstrong Numbers

- All single-digit numbers (0-9) are Armstrong numbers, as each number is equal to itself raised to the power of 1.
- There are four 3-digit Armstrong numbers: 153, 370, 371, and 407.
- The number of Armstrong numbers is finite. As the number of digits increases, the sum of the digits raised to the power of the number of digits becomes smaller relative to the actual number.

Now that we have an understanding of what an Armstrong number is and its properties, let's move on to implementing a program to find Armstrong numbers in C.

## Checking for Armstrong Numbers in C

To check if a given number is an Armstrong number, we need to perform the following steps:

- Find the number of digits in the number.
- Calculate the sum of the digits, each raised to the power of the number of digits.
- Compare the sum with the original number. If they are equal, the number is an Armstrong number; otherwise, it is not.

Let's start by implementing a function to find the number of digits in a given number.

### Finding the Number of Digits

We can easily find the number of digits in a number by repeatedly dividing it by 10 until the result is less than 1. The number of divisions required gives us the number of digits in the number.

Here's the code implementation:

`#include <stdio.h> int count_digits(int num) { int count = 0; while (num != 0) { num /= 10; count++; } return count; } int main() { int number = 153; printf("Number of digits in %d: %d\n", number, count_digits(number)); return 0; }`

This code defines a function `count_digits`

that takes an integer `num`

as input and returns the number of digits in it. The main function demonstrates how to use this function by calling it with an example number (153) and printing the result.

Now that we can find the number of digits in a number, let's move on to calculating the sum of the digits, each raised to the power of the number of digits.

### Calculating the Sum of Digits Raised to the Power of Number of Digits

To calculate the sum of the digits, each raised to the power of the number of digits, we can extract each digit by taking the modulus with 10 and then divide the number by 10 to get the remaining digits. We then raise the extracted digit to the power of the number of digits and add it to the sum. We repeat this process until the number becomes 0.

Here's the code implementation:

`#include <math.h> #include <stdio.h> int count_digits(int num) { // ... (code as before) } int sum_of_digits_raised_to_power(int num, int power) { int sum = 0; while (num != 0) { int digit = num % 10; sum += pow(digit, power); num /= 10; } return sum; } int main() { int number = 153; int num_digits = count_digits(number); printf("Sum of digits of %d raised to power %d: %d\n", number, num_digits, sum_of_digits_raised_to_power(number, num_digits)); return 0; }`

This code defines a new function `sum_of_digits_raised_to_power`

that takes an integer `num`

and an integer `power`

as input and returns the sum of the digits of `num`

, each raised to the power of `power`

. The main function demonstrates how to use this function by calling it with an example number (153) and the number of digits in that number, and then printing the result.

Now that we can calculate the sum of the digits, each raised to the power of the number of digits, let's move on to checking if a number is an Armstrong number.

### Checking if a Number is an Armstrong Number

To check if a number is an Armstrong number, we can use the functions we have implemented so far to find the number of digits and calculate the sum of the digits, each raised to the power of the number of digits. If the sum is equal to the original number, it is an Armstrong number; otherwise, it is not.

Here's the complete code implementation:

`#include <math.h> #include <stdbool.h> #include <stdio.h> int count_digits(int num) { // ... (code as before) } int sum_of_digits_raised_to_power(int num, int power) { // ... (code as before) } bool is_armstrong_number(int num) { int num_digits = count_digits(num); int sum = sum_of_digits_raised_to_power(num, num_digits); return sum == num; } int main() { int number = 153; printf("%d is an Armstrong number: %s\n", number, is_armstrong_number(number) ? "Yes" : "No"); return 0; }`

This code defines a new function `is_armstrong_number`

that takes an integer `num`

as input and returns a boolean value indicating whether `num`

is an Armstrong number. The main function demonstrates how to use this function by calling it with an example number (153) and printing the result.

## Frequently Asked Questions (FAQ)

### What is the time complexity of the Armstrong number algorithm?

The time complexity of the Armstrong number algorithm is O(n), where n is the number of digits in the number. This is because we need to iterate through each digit of the number to calculate the sum of the digits raised to the power of the number of digits.

### Are there any variations or optimizations to the Armstrong number algorithm?

Yes, there are variations of the Armstrong number algorithm that can make the code more efficient or concise. For example, you can use a recursive function to calculate the sum of the digits raised to the power of the number of digits, or you can use a lookup table to store the powers of the digits to avoid recalculating them each time.

### How can I find all Armstrong numbers within a given range?

To find all Armstrong numbers within a given range, you can iterate through all the numbers in the range and check if each number is an Armstrong number using the `is_armstrong_number`

function we implemented earlier. If a number is an Armstrong number, add it to a list or print it out.

Yes, there are similar number types and problems in mathematics and programming that involve digit manipulation, such as finding perfect numbers, abundant numbers, deficient numbers, or happy numbers. These problems often have similar algorithmic approaches to the Armstrong number problem and can be good practice for programmers to improve their skills.

## Conclusion

In this blog post, we have learned about Armstrong numbers, their properties, and how to implement a program to find Armstrong numbers in C. We have provided detailed explanations and code examples to help you grasp the concepts easily. We hope this guide has been helpful for you, and you can now confidently tackle problems related to Armstrong numbers in your programming journey.

For further reading and resources on C programming and mathematics, you can refer to the C Programming Language documentation and the Wikipedia page on Armstrong numbers. Happy coding!

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