C Program to find the given number is strong or not

A strong number is a number where the sum of the factorial of its digits equals the number itself. For example, 145 is a strong number because 1! + 4! + 5! = 1 + 24 + 120 = 145.

Syntax

int factorial(int n);
int isStrongNumber(int num);

Understanding Strong Numbers

Let's examine some examples to understand the concept better ?

145 = 1! + 4! + 5!
    = 1 + 24 + 120
    = 145 (Strong number)

123 = 1! + 2! + 3!
    = 1 + 2 + 6
    = 9 (Not a strong number)

Example: Check if Number is Strong

This program calculates the sum of factorials of each digit and compares it with the original number ?

#include <stdio.h>

int main() {
    int n, temp, rem, sum = 0, i, fact;
    
    printf("Enter a number: ");
    n = 145;  /* Testing with 145 */
    temp = n;

    while (n) {
        i = 1;
        fact = 1;
        rem = n % 10;
        
        /* Calculate factorial of digit */
        while (i <= rem) {
            fact = fact * i;
            i++;
        }
        
        sum = sum + fact;
        n = n / 10;
    }

    if (sum == temp)
        printf("%d is a strong number<br>", temp);
    else
        printf("%d is not a strong number<br>", temp);

    return 0;
}

145 is a strong number

Example: Testing Multiple Numbers

Here's a program that tests several numbers to demonstrate strong number identification ?

#include <stdio.h>

int factorial(int n) {
    int fact = 1;
    for (int i = 1; i <= n; i++) {
        fact = fact * i;
    }
    return fact;
}

int isStrongNumber(int num) {
    int sum = 0, temp = num;
    
    while (num > 0) {
        int digit = num % 10;
        sum = sum + factorial(digit);
        num = num / 10;
    }
    
    return (sum == temp);
}

int main() {
    int numbers[] = {1, 2, 145, 40585, 123};
    int size = 5;
    
    for (int i = 0; i < size; i++) {
        if (isStrongNumber(numbers[i]))
            printf("%d is a strong number<br>", numbers[i]);
        else
            printf("%d is not a strong number<br>", numbers[i]);
    }
    
    return 0;
}

1 is a strong number
2 is a strong number
145 is a strong number
40585 is a strong number
123 is not a strong number

Key Points

• Strong numbers are rare − only a few exist like 1, 2, 145, and 40585.
• The algorithm extracts each digit using modulo 10 and integer division.
• Factorial calculation can be optimized by precomputing factorials 0! to 9!.

Conclusion

A strong number check involves calculating factorials of individual digits and comparing their sum with the original number. This mathematical property makes strong numbers quite rare and interesting to study.