Python Program to Check Automorphic Number

Posted in Python Tutorial

Updated on Oct 31, 2024

By Mari Selvan

👁️ 114 - Views

⏳ 4 mins

💬 1 Comment

Python Program to Check Automorphic Number

Photo Credit to CodeToFun

🙋 Introduction

In the realm of python programming, exploring unique number properties is both fascinating and educational. An automorphic number is one such interesting concept.

An automorphic number (or circular number) is a number whose square ends with the number itself. In simpler terms, an n-digit number is called an automorphic number if the last n digits of its square are equal to the number itself.

In this tutorial, we'll delve into a Python program that checks whether a given number is an automorphic number or not.

The program will take a number as input, square it, and then compare the last digits to determine if it meets the criteria of an automorphic number.

📄 Example

Let's explore the Python code that accomplishes this task.

is_automorphic.py

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def is_automorphic(num):
    # Calculate the square of the number
    square = num ** 2

    # Count the number of digits in the original number
    original_digits = len(str(num))

    # Extract the last digits from the square
    last_digits = square % 10**original_digits

    # Check if the last digits match the original number
    return last_digits == num

# Driver program
if __name__ == "__main__":
    # Replace this value with your desired number
    number = 76

    # Check if the number is automorphic
    if is_automorphic(number):
        print(f"{number} is an automorphic number.")
    else:
        print(f"{number} is not an automorphic number.")

💻 Testing the Program

To test the program with different numbers, simply replace the value of number in the if __name__ == "__main__": block.

Output

76 is an automorphic number.

Run the script to check if the given number is an automorphic number.

🧠 How the Program Works

The program defines a function is_automorphic that takes a number as input and returns whether it is an automorphic number or not.
Inside the function, it calculates the square of the input number.
It counts the number of digits in the original number to extract the corresponding number of last digits from the square.
It compares the extracted last digits with the original number to determine if it's an automorphic number.

📏 Between the Given Range

Let's explore the Python code that identifies Automorphic Numbers within the specified range.

is_automorphic.py

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# Function to check if a number is Automorphic
def is_automorphic(num):
    square = num ** 2
    str_num = str(num)
    str_square = str(square)

    return str_square.endswith(str_num)

# Check Automorphic Numbers in the range 1 to 50
automorphic_numbers = [num for num in range(1, 51) if is_automorphic(num)]

# Display the results
print("Automorphic Numbers in the Range 1 to 50:")
for num in automorphic_numbers:
    print(num, end=" ")

💻 Testing the Program

Output

Automorphic Numbers in the Range 1 to 50:
1 5 6 25

Run the Python script, and it will display the Automorphic Numbers in the range of 1 to 50.

🧠 How the Program Works

The program defines a function is_automorphic that takes a number as input, calculates its square, and checks if the square ends with the same digits as the original number.
It then uses a list comprehension to generate a list of Automorphic Numbers within the range of 1 to 50.
Finally, the program prints the identified Automorphic Numbers.

🧐 Understanding the Concept of Automorphic Numbers

Before delving into the code, let's take a moment to understand automorphic numbers.

An n-digit number is called an automorphic number if the last n digits of its square are equal to the number itself.

For example, 25 is an automorphic number because its square is 625, and the last two digits (25) match the original number.

🎢 Optimizing the Program

While the provided program effectively checks for automorphic numbers, you can explore and implement further optimizations or variations based on your specific needs or preferences.

Feel free to incorporate and modify this code as needed for your specific use case. Happy coding!