What is a Strong (Krishnamurthy) Number?

A Strong Number (also known as a Krishnamurthy Number or Peterson Number) is a special integer whose sum of the factorials of its digits equals the original number.

Example:

For $n = 145$:

text (ISO Standard)
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1! + 4! + 5! = 1 + 24 + 120 = 145

Since the sum equals 145, 145 is a Strong Number.

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Working C Code

c (ISO Standard)
Run in Compiler.cCopy
#include <stdio.h>
#include <stdbool.h>

/* Precomputed digit factorials (0! through 9!) */
static const int FACTORIALS[10] = {
    1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880
};

bool isStrongNumber(int n) {
    if (n <= 0) return false;

    int original = n;
    int sum = 0;
    int temp = n;

    while (temp > 0) {
        int digit = temp % 10;
        sum += FACTORIALS[digit];
        temp /= 10;
    }

    return sum == original;
}

int main() {
    int testCases[] = {1, 2, 145, 40585, 123, 500};
    int count = sizeof(testCases) / sizeof(testCases[0]);

    printf("Strong Number Verification in C:\n\n");
    for (int i = 0; i < count; i++) {
        int num = testCases[i];
        if (isStrongNumber(num)) {
            printf("  %d -> STRONG NUMBER\n", num);
        } else {
            printf("  %d -> Not a strong number\n", num);
        }
    }

    return 0;
}

Sample Output

text (ISO Standard)
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Strong Number Verification in C:

  1 -> STRONG NUMBER
  2 -> STRONG NUMBER
  145 -> STRONG NUMBER
  40585 -> STRONG NUMBER
  123 -> Not a strong number
  500 -> Not a strong number

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Complexity Analysis

• Time Complexity: O(log₁₀ n) digit extractions.
• Space Complexity: O(1) constant space using precomputed factorials.

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Related Guides

• Review factorial loops in Factorial Program in C.
• Compare with digit power sums in Armstrong Number in C.