Check Automorphic Number in Java: Logic + Full Code (2026)

Introduction

An automorphic number is a genuinely elegant special-number category. It asks whether squaring a number produces a result that ends with the original number itself, almost as if the number leaves its own signature at the end of its square.

It pairs nicely with the Neon Number problem because both involve squaring a number. However, the comparison rule is completely different:

• Neon Number: Compare the original number with the sum of the digits of its square.
• Automorphic Number: Check whether the square ends with the original number.

In this guide, you'll learn:

• What an automorphic number is
• How to check it using a numeric (modulus-based) approach
• How to solve it using String.endsWith()
• How to print all automorphic numbers within a range
• Why matching the correct digit count is the trickiest part of the numeric approach
• Best practices, interview tips, common mistakes, and FAQs

What Is an Automorphic Number?

A number is called an automorphic number if its square ends with the number itself.

For example, consider 25.

Its square is:

25² = 625

Notice that 625 ends with 25.

Therefore, 25 is an automorphic number.

Another well-known example is 76.

76² = 5776

Again, the square ends with 76.

Therefore:

76 is also an automorphic number.

Some other automorphic numbers include:

1
5
6
25
76
376
625
9376

Method 1: Using a Numeric (Modulus-Based) Approach

This approach avoids converting numbers into strings.

Instead, it extracts the required number of trailing digits from the square using the modulus (%) operator and compares them with the original number.

public class AutomorphicNumeric {

    public static void main(String[] args) {

        int num = 25;

        long square = (long) num * num;

        int digitCount = String.valueOf(num).length();

        long divisor = (long) Math.pow(10, digitCount);

        long lastDigits = square % divisor;

        if (lastDigits == num) {
            System.out.println(num + " is an automorphic number.");
        } else {
            System.out.println(num + " is not an automorphic number.");
        }
    }
}

How This Works

The algorithm performs four simple steps.

Step 1: Calculate the Square

For the input:

25

the square becomes:

625

Step 2: Count the Number of Digits

The original number has:

25 → 2 digits

Therefore:

digitCount = 2;

Step 3: Create the Divisor

The divisor is calculated as:

10digitCount

For two digits:

10² = 100

So:

divisor = 100;

Step 4: Extract the Last Digits

Now calculate:

625 % 100 = 25

The extracted value is:

25

Finally, compare:

25 == 25

Since they are equal, the number is automorphic.

Output

25 is an automorphic number.

Why We Use long for the Square

A common beginner mistake is storing the square in an int.

For example:

int square = num * num;

This works for small numbers but may overflow for larger values because Java's int data type has a maximum value of:

2,147,483,647

Squaring even moderately large integers can exceed this limit.

Instead, use:

long square = (long) num * num;

Using long greatly increases the available range and helps prevent integer overflow.

The same applies to the divisor and any calculations involving the squared value.

Method 2: Using String.endsWith() (Simpler Approach)

A much simpler solution converts both the original number and its square into strings and checks whether the square ends with the original number.

public class AutomorphicString {

    public static void main(String[] args) {

        int num = 76;

        long square = (long) num * num;

        String numStr = String.valueOf(num);
        String squareStr = String.valueOf(square);

        if (squareStr.endsWith(numStr)) {
            System.out.println(num + " is an automorphic number.");
        } else {
            System.out.println(num + " is not an automorphic number.");
        }
    }
}

How This Works

First, the program calculates the square.

For example:

76² = 5776

The program then converts both values into strings:

numStr = "76"

squareStr = "5776"

Finally, it performs the comparison:

squareStr.endsWith(numStr)

which is equivalent to asking:

"Does 5776 end with 76?"

The answer is Yes, so 76 is an automorphic number.

Output

76 is an automorphic number.

Why This Approach Is Simpler

The endsWith() method directly matches the mathematical definition of an automorphic number.

Instead of manually:

• Counting digits
• Calculating powers of 10
• Computing divisors
• Extracting trailing digits using modulus

you simply ask whether one string ends with another.

This makes the code:

• Easier to read
• Easier to understand
• Less error-prone
• Easier to maintain

For most real-world Java programs, the String.endsWith() approach is generally the preferred solution because it is concise and clearly expresses the intent of the algorithm.

Method 3: Printing All Automorphic Numbers in a Range

To find every automorphic number within a range, place the automorphic number check inside a reusable method and call it for every number in the specified range.

The following example uses the simpler String.endsWith() approach.

public class AutomorphicInRange {

    static boolean isAutomorphic(int num) {

        long square = (long) num * num;

        String numStr = String.valueOf(num);
        String squareStr = String.valueOf(square);

        return squareStr.endsWith(numStr);
    }

    public static void main(String[] args) {

        int start = 1;
        int end = 10000;

        System.out.println("Automorphic numbers between " + start + " and " + end + ":");

        for (int num = start; num <= end; num++) {
            if (isAutomorphic(num)) {
                System.out.print(num + " ");
            }
        }
    }
}

Output

Automorphic numbers between 1 and 10000:
1 5 6 25 76 376 625 9376

How This Works

Instead of checking a single number, the program loops through every number in the specified range.

For each number:

1. The isAutomorphic() method calculates its square.
2. Both the number and its square are converted into strings.
3. The endsWith() method checks whether the square ends with the original number.
4. If the method returns true, the number is printed.

Because the checking logic is placed inside a reusable method, the program remains clean and easy to maintain.

Why Are Automorphic Numbers Rare?

Unlike Harshad numbers, which appear frequently, automorphic numbers are surprisingly rare.

Within the first 10,000 positive integers, there are only:

1
5
6
25
76
376
625
9376

Only 8 numbers satisfy the automorphic property in this range.

This makes automorphic numbers similar to Armstrong numbers and Strong numbers, where only a small number of values satisfy the required mathematical condition.

Why the Numeric Approach Requires Matching Digit Counts

The numeric (modulus-based) solution has one tricky requirement.

It must extract exactly the same number of trailing digits as the original number contains.

If the digit count is incorrect, the comparison also becomes incorrect.

Correct Example

Consider the number:

25

Its square is:

625

Since 25 has 2 digits, the divisor should be:

10² = 100

Now calculate:

625 % 100 = 25

The extracted value matches the original number.

Therefore, 25 is automorphic.

What Happens If the Digit Count Is Wrong?

Suppose we accidentally use:

100

as the divisor for every number.

Now consider the number:

5

Its square is:

25

Using the incorrect divisor:

25 % 100 = 25

The comparison becomes:

25 == 5

which is false.

The program would incorrectly conclude that 5 is not automorphic.

However, this is wrong.

Since 5 has only one digit, we should have used:

10¹ = 10

Now calculate:

25 % 10 = 5

The comparison becomes:

5 == 5

which correctly identifies 5 as an automorphic number.

Why the String Approach Avoids This Problem

The endsWith() method automatically compares the correct number of trailing characters.

For example:

"625".endsWith("25")

returns:

true

Likewise:

"25".endsWith("5")

also returns:

true

No digit counting, powers of ten, or modulus calculations are required.

This is one of the biggest reasons why the string-based solution is generally preferred.

How Java Handles This Internally (Memory Concept)

Although both approaches solve the same problem, Java handles them differently behind the scenes.

Method 1 (Numeric Approach)

The following variables are primitive values:

• num
• square
• digitCount
• divisor
• lastDigits

These variables are stored inside the stack frame of the currently executing method.

The expression:

square % divisor

performs a simple arithmetic operation directly on primitive values.

No objects are created while performing the comparison.

The call to:

Math.pow(10, digitCount)

internally performs a floating-point calculation and returns a double, which is then cast to a long.

Apart from this calculation, the numeric approach uses only primitive variables.

Methods 2 and 3 (String Approach)

The string-based solution creates two String objects:

String numStr = String.valueOf(num);

String squareStr = String.valueOf(square);

These strings are allocated on the heap memory.

The endsWith() method then compares the characters from the end of squareStr with those in numStr.

Internally, Java performs a character-by-character comparison until either:

• Every character matches, or
• A mismatch is found.

Although this involves creating String objects, the memory overhead is very small for typical integer values.

Overall Memory Usage

Neither solution uses:

• Arrays
• Collections
• Recursion
• Complex data structures

The numeric solution relies entirely on primitive arithmetic.

The string solution creates only two small String objects.

Both approaches are therefore efficient and suitable for practical applications, with the string approach generally offering better readability and simpler implementation.

Real-Life Analogy: A Reflection That Preserves Your Signature

Imagine writing your signature at the end of an important document.

Now imagine that document is copied, expanded, or transformed into a much larger version.

Most of the time, your original signature would either disappear or become buried somewhere in the middle of the new document.

Occasionally, however, the transformed document still ends with your exact original signature.

That is the idea behind an automorphic number.

Squaring the number creates a much larger value, but the original number still appears unchanged at the very end of its square.

It is almost as if the original number leaves its own signature behind.

Comparison Table of All Methods

Best Practices

Following these best practices will help you write clean, efficient, and reliable automorphic number programs.

• Prefer the String.endsWith() approach for most situations. It is simpler, easier to read, and automatically handles numbers with different digit lengths.
• Always store the square in a long rather than an int to reduce the risk of integer overflow when squaring larger values.
• If you choose the numeric approach, carefully calculate the digit count of the original number, not the square. An incorrect digit count results in an incorrect divisor and produces wrong answers.
• Wrap the checking logic inside a reusable method such as:

boolean isAutomorphic(int num)

This improves readability and makes the code easier to reuse throughout your application.

• Test your implementation using several known automorphic numbers such as:

1
5
6
25
76
376
625
9376

Testing multiple known values helps confirm that your implementation is working correctly.

Common Mistakes Beginners Make

Although the algorithm is straightforward, beginners frequently make a few common mistakes.

1. Using the Wrong Divisor

A common mistake in the numeric approach is using a fixed divisor such as:

100

for every number.

Different numbers have different digit counts, so the divisor must also change accordingly.

Always calculate:

10digitCount

based on the number of digits in the original number.

2. Storing the Square in an int

Some beginners write:

int square = num * num;

For larger values, this can overflow because an int has a limited range.

Instead, write:

long square = (long) num * num;

This greatly increases the range of values that can be handled safely.

3. Confusing Automorphic Numbers with Neon Numbers

Both problems involve squaring a number, but they check completely different conditions.

Understanding this distinction prevents unnecessary implementation mistakes.

4. Assuming Automorphic Numbers Are Common

Many beginners expect to find large numbers of automorphic values within a range.

In reality, they are quite rare.

For example, between 1 and 10,000, only:

1
5
6
25
76
376
625
9376

are automorphic numbers.

5. Overcomplicating the Solution

Some implementations perform unnecessary calculations involving:

• Digit extraction
• Loops
• Manual suffix comparisons

When a simple call to:

endsWith()

already expresses the problem directly.

Whenever appropriate, prefer the simpler and more readable solution.

Expert Tips for Interviews

A strong interview answer should explain both the recommended solution and the arithmetic alternative.

A complete response might sound like this:

"An automorphic number is one whose square ends with the original number. The simplest solution is to convert both values into strings and use String.endsWith(), which directly expresses the definition of the problem. Another approach avoids strings by calculating the original number's digit count, extracting the same number of trailing digits from the square using the modulus operator, and comparing the result with the original number. When using the arithmetic approach, it's important to calculate the correct divisor and store the square in a long to avoid overflow."

Mentioning both solutions—and explaining why the string-based approach is generally preferred—demonstrates practical judgment as well as a solid understanding of the underlying mathematics.

Pros and Cons

Numeric (Modulus-Based) Approach

Pros

• ✅ Avoids string conversion
• ✅ Uses only arithmetic operations
• ✅ Good for practicing digit manipulation
• ✅ Demonstrates understanding of modulus and powers of ten

Cons

• ❌ More difficult to implement correctly
• ❌ Requires careful digit-count calculation
• ❌ Easier to introduce subtle bugs

String.endsWith() Approach

Pros

• ✅ Very simple and readable
• ✅ Directly matches the mathematical definition
• ✅ Automatically handles different digit lengths
• ✅ Less error-prone than the numeric approach

Cons

• ❌ Creates small String objects
• ❌ Slight overhead from string conversion (generally negligible for normal inputs)

Frequently Asked Questions (FAQs)

1. What is an automorphic number?

An automorphic number is a number whose square ends with the original number itself.

For example:

25² = 625

Since 625 ends with 25, 25 is an automorphic number.

2. What are some known automorphic numbers?

Some well-known automorphic numbers are:

1
5
6
25
76
376
625
9376

These are the automorphic numbers between 1 and 10,000.

3. What is the simplest way to check an automorphic number in Java?

The easiest approach is to:

1. Calculate the square of the number.
2. Convert both the number and its square to strings.
3. Use the endsWith() method.

For example:

String numStr = String.valueOf(num);
String squareStr = String.valueOf(square);

if (squareStr.endsWith(numStr)) {
    System.out.println("Automorphic Number");
}

This approach is simple, readable, and automatically handles numbers with different digit lengths.

4. How do I check an automorphic number without using strings?

You can use a purely arithmetic approach.

The steps are:

1. Count the number of digits in the original number.
2. Calculate the divisor (10digitCount).
3. Extract the last digits using the modulus operator.
4. Compare the extracted value with the original number.

For example:

long lastDigits = square % divisor;

If:

lastDigits == num

the number is automorphic.

5. Why should I use long instead of int for the squared value?

Squaring even moderately large integers can exceed the maximum value of an int.

For example:

long square = (long) num * num;

Using long reduces the risk of integer overflow and allows the program to work correctly for much larger inputs.

6. What is the difference between an automorphic number and a neon number?

Although both involve squaring a number, they use different conditions.

7. Are automorphic numbers common or rare?

Automorphic numbers are relatively rare.

Only the following numbers are automorphic between 1 and 10,000:

1
5
6
25
76
376
625
9376

Compared with Harshad numbers, they occur much less frequently.

8. What is the time complexity of checking an automorphic number?

For both approaches, the running time is very small.

• The arithmetic calculations are constant time for fixed-size integers.
• The string-based approach performs a comparison proportional to the number of digits.

Overall, the time complexity is effectively O(d), where d is the number of digits.

The space complexity is:

• O(1) for the numeric approach.
• O(d) for the string-based approach because small String objects are created.

9. Can I find all automorphic numbers within a range in Java?

Yes.

Simply loop through every number in the range and call a reusable method such as:

isAutomorphic(num)

If the method returns true, print the number.

For example:

for (int num = start; num <= end; num++) {
    if (isAutomorphic(num)) {
        System.out.print(num + " ");
    }
}

10. Is checking for automorphic numbers a common interview question?

It is less common than questions involving prime numbers, Armstrong numbers, or palindromes, but it still appears occasionally in interviews involving digit manipulation and mathematical logic.

Interviewers may also ask candidates to compare:

• A numeric solution
• A string-based solution

and explain the advantages of each.

11. Why might the numeric approach fail if the digit count is calculated incorrectly?

The numeric solution depends entirely on extracting the correct number of trailing digits.

If the divisor is incorrect, the wrong digits are extracted.

For example:

25² = 625

Using:

625 % 100 = 25

correctly identifies 25 as automorphic.

However, for the number 5, using:

25 % 100 = 25

would incorrectly compare:

25 == 5

and produce the wrong result.

The correct divisor for 5 is 10, giving:

25 % 10 = 5

which correctly identifies 5 as automorphic.

12. Is 0 considered an automorphic number?

Yes.

By convention:

0² = 0

Since 0 ends with 0, the number satisfies the automorphic number definition.

Some textbooks begin their examples from 1, while others include 0.

Both conventions are commonly accepted as long as the definition is stated clearly