C Program to check Strong Number

A Strong Number is a number whose sum of the factorials of its digits equals the original number. For example, 145 is a strong number because 1! + 4! + 5! = 1 + 24 + 120 = 145.

Syntax

int factorial(int digit);
int isStrongNumber(int number);

Algorithm

• Extract each digit from the number starting from the unit place
• Calculate the factorial of each digit
• Sum all the factorials
• Compare the sum with the original number

Example

Let's implement a C program to check if a number is a Strong Number −

#include <stdio.h>

int factorial(int r) {
    int fact = 1;
    while(r > 1) {
        fact = fact * r;
        r--;
    }
    return fact;
}

int isStrongNumber(int n) {
    int temp, rem, result = 0;
    temp = n;
    while(temp) {
        rem = temp % 10;
        result = result + factorial(rem);
        temp = temp / 10;
    }
    if (result == n)
        return 1;
    else
        return 0;
}

int main() {
    int n = 145;
    printf("Number: %d<br>", n);
    if (isStrongNumber(n))
        printf("Yes, it is a strong number<br>");
    else
        printf("No, it is not a strong number<br>");
    
    // Test with another number
    n = 124;
    printf("\nNumber: %d<br>", n);
    if (isStrongNumber(n))
        printf("Yes, it is a strong number<br>");
    else
        printf("No, it is not a strong number<br>");
    
    return 0;
}

Number: 145
Yes, it is a strong number

Number: 124
No, it is not a strong number

How It Works

• For 145: 1! + 4! + 5! = 1 + 24 + 120 = 145 (Strong Number)
• For 124: 1! + 2! + 4! = 1 + 2 + 24 = 27 ? 124 (Not a Strong Number)

Key Points

• The factorial function calculates the factorial of a single digit (0-9)
• We extract digits using modulo (%) and integer division (/) operations
• Common strong numbers include: 1, 2, 145, and 40585

Conclusion

A Strong Number is identified by comparing the sum of factorials of its digits with the original number. The algorithm efficiently extracts digits and computes factorials to perform this verification.