C Program to Find an Automorphic Number

In C, an automorphic number is a positive integer whose square ends with the number itself. For example, 5² = 25 (ends with 5), and 25² = 625 (ends with 25). This article demonstrates how to check whether a given number is automorphic in C programming.

Syntax

int isAutomorphicNumber(int num);

Examples of Automorphic Numbers

Consider the following examples to understand automorphic numbers

• 5: 5² = 25 (ends with 5) Automorphic
• 25: 25² = 625 (ends with 25) Automorphic
• 7: 7² = 49 (ends with 49, not 7) Not Automorphic

Method 1: Iterative Digit Comparison

This approach compares the last digits of the number and its square iteratively using division and modulo operations

#include <stdio.h>

int isAutomorphicNumber(int num) {
    int square = num * num;
    
    while (num > 0) {
        if (num % 10 != square % 10) {
            return 0;  // Not automorphic
        }
        num /= 10;
        square /= 10;
    }
    return 1;  // Automorphic
}

int main() {
    int number = 25;
    
    printf("Number: %d<br>", number);
    printf("Square: %d<br>", number * number);
    
    if (isAutomorphicNumber(number)) {
        printf("%d is an Automorphic Number<br>", number);
    } else {
        printf("%d is not an Automorphic Number<br>", number);
    }
    
    return 0;
}

Number: 25
Square: 625
25 is an Automorphic Number

Method 2: Mathematical Modulo Approach

This approach counts the digits in the number and uses the modulo operation with 10^d to extract the last d digits from the square

#include <stdio.h>

int countDigits(int num) {
    int count = 0;
    while (num > 0) {
        count++;
        num /= 10;
    }
    return count;
}

int power(int base, int exp) {
    int result = 1;
    for (int i = 0; i < exp; i++) {
        result *= base;
    }
    return result;
}

int isAutomorphicNumber(int num) {
    int square = num * num;
    int digits = countDigits(num);
    int divisor = power(10, digits);
    
    return (square % divisor == num);
}

int main() {
    int number = 5;
    
    printf("Number: %d<br>", number);
    printf("Square: %d<br>", number * number);
    
    if (isAutomorphicNumber(number)) {
        printf("%d is an Automorphic Number<br>", number);
    } else {
        printf("%d is not an Automorphic Number<br>", number);
    }
    
    return 0;
}

Number: 5
Square: 25
5 is an Automorphic Number

Comparison

Conclusion

Both methods effectively determine automorphic numbers with O(d) time complexity, where d is the number of digits. The iterative approach is simpler while the modulo approach provides a more mathematical solution.