🔢 Kaprekar_Routine

This repository demonstrates the famous Kaprekar’s Routine in C, implemented for both 3-digit and 4-digit numbers.

Kaprekar's Routine is a process in recreational mathematics that repeatedly rearranges digits and subtracts numbers to reach a fixed point, known as the Kaprekar Constant.

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📁 Files

• Kaprekar_Routine_3.c
  Implementation of Kaprekar's routine for 3-digit numbers.
  Constant reached: 495

• Kaprekar_Routine_4.c
  Implementation of Kaprekar's routine for 4-digit numbers.
  Constant reached: 6174

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🧠 How It Works

Steps of Kaprekar's Routine:

1. Take a number with at least two different digits.
2. Rearrange its digits to form the largest and smallest possible numbers.
3. Subtract the smaller number from the larger.
4. Repeat the process with the result.
5. Eventually, the number converges to a fixed constant.

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🔍 Kaprekar Constants

Digits	Constant	Example Start	Steps to Reach
3-digit	495	321 → 198 → ... → 495	≤ 6 steps
4-digit	6174	3524 → 3087 → ... → 6174	≤ 7 steps

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⚠️ Notes

• The input number must have at least two different digits.
• If all digits are the same (e.g., 1111 or 777), the result is always zero, and the routine doesn't proceed.
• Leading zeros are handled in sorting, but not preserved in numeric values (e.g., 0009 → 9).

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🛠️ How to Compile & Run

Using GCC:

gcc Kaprekar_Routine_3.c -o kap3
./kap3

gcc Kaprekar_Routine_4.c -o kap4
./kap4

📄 License

This project is open-source and free to use for educational and learning purposes.

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