Magical Subtraction

Kaprekar’s Constant, is a magical mathematical phenomenon that makes subtraction a whole lot of fun! It is named after the Indian mathematician D.R. Kaprekar, and is a number that, when you subtract its digits and repeat the process, always converges to the number 6174. Year 4 students investigated this intriguing concept that not only reinforces subtraction skills but also encourages them to pay close attention to the step-by-step instructions. And it’s so much fun, they asked to try and try again. Do your students need practice with subtraction? Turn to Kaprekar. Instructions below.


Step 1: Choose a Four-Digit Number

  • Select any four-digit number, ensuring that it has at least two distinct digits (e.g., avoid numbers like 1111 or 2222).

Step 2: Rearrange the Digits

  • Rearrange the digits of the chosen number to create the largest and smallest possible numbers. You can rearrange the digits in ascending (from smallest to largest) or descending (from largest to smallest) order.

Step 3: Subtract the Smallest Number from the Largest Number

  • Subtract the smaller number from the larger number.

Step 4: Repeat the Process

  • Take the result from Step 3 and repeat the process. Rearrange the digits to create the largest and smallest possible numbers and subtract them again.

Step 5: Continue until You Reach 6174

  • Keep repeating the process until you reach the number 6174. Once you reach 6174, the process will continue to result in 6174 for each subsequent iteration.

It’s important to note that Kaprekar’s Constant is always reached within a few iterations, regardless of the starting number. If you find that the process is not converging to 6174, ensure that you’re correctly following the steps and that you’re using a four-digit number with at least two distinct digits.

Kaprekar’s Constant is a fun way to engage in mathematical exploration and problem-solving, and it can be an enjoyable activity for both children and adults interested in mathematics.

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