Java Programs›Numbers›Check Automorphic Number

Check Automorphic Number in Java

beginner· Numbers · Number Theory

Problem

An automorphic number is a number that appears unchanged as the trailing digits of its own square.

Given a number, determine whether it is an automorphic number.

Input

76

Output

76 is an automorphic number: true

Java Program

Java

public class AutomorphicCheck {
    public static void main(String[] args) {
        int num = 76;
        long square = (long) num * num; // avoid int overflow on larger inputs
        String numStr = String.valueOf(num);
        String squareStr = String.valueOf(square);

        boolean isAutomorphic = squareStr.endsWith(numStr);
        System.out.println(num + " is an automorphic number: " + isAutomorphic);
    }
}

▶ Run Code

Output

76 is an automorphic number: true

Core Logic

Squaring the number and checking whether the square's string representation ends with the original number's digits answers the question directly.

How It Works

1square is computed as num * num, cast to a long to avoid overflow on larger inputs.
2String.valueOf(square) and String.valueOf(num) convert both values into text.
3.endsWith(numStr) checks whether the square's digits end with exactly the original number's digits.

For 76, the square is 5776, whose text representation "5776" ends with "76" — a match.

💡

Key Point: Casting to long before squaring matters for larger automorphic numbers — an int square can silently overflow well before the number itself looks large.

Complexity

Time Complexity: O(1)Space Complexity: O(1)

Why: Squaring and formatting a fixed-size number are both constant-time operations that don't scale with the number's magnitude in any meaningful way for typical input sizes.

Key Concepts

String.endsWith()squaringdigit count

Approach 2: Without String Conversion

Java

public class AutomorphicCheckArithmetic {
    public static void main(String[] args) {
        int num = 76;
        long square = (long) num * num;
        int digitCount = String.valueOf(num).length();
        long divisor = (long) Math.pow(10, digitCount);

        // Extracts the last digitCount digits of the square using modulo
        boolean isAutomorphic = (square % divisor) == num;
        System.out.println(num + " is an automorphic number: " + isAutomorphic);
    }
}

▶ Run Code

Output

76 is an automorphic number: true

Core Logic

The same trailing-digits check can be done with pure arithmetic — take the square modulo a power of 10 matching the original number's digit count.

How It Works

1digitCount is found from String.valueOf(num).length(), purely to size the modulo divisor — no string comparison happens.
2Math.pow(10, digitCount) computes the divisor: 10 raised to the digit count, e.g. 100 for a 2-digit number.
3square % divisor extracts exactly the last digitCount digits of the square.
4That remainder is compared directly against the original number.

For 76, digitCount is 2, so the divisor is 100; 5776 % 100 = 76, which matches the original number.

💡

Key Point: This avoids building any String objects at all — the comparison stays entirely in the numeric domain, which matters more for very large numbers checked repeatedly.

Complexity

Time Complexity: O(1)Space Complexity: O(1)

Why: The modulo and power operations run in constant time regardless of the number's magnitude, with no string allocation involved.

Key Concepts

modulo arithmeticMath.pow()arithmetic-only comparison

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