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Kaprekar Constant 495 for Three-digit Number

Dattatreya Ramchandra Kaprekar (D. R. Kaprekar; 1905 – 1986) was an Indian mathematician who discovered several classes of natural numbers including Kaprekar Constant.

The number 495 is called Kaprekar Constant for three-digit number.

Why is the number 495 called Kaprekar Constant?

In 1949, D. R. Kaprekar discovered an interesting property of the number 495 through the mathematical calculations.

D. R. Kaprekar observed that when any three-digit number of non-identical digits (not all digits are same) is arranged in two parts – highest number and lowest number, and difference is calculated using subtraction method, then the end-result will be always 495.

If the process is continued even after getting the end-result 495, then the end-result will be always 495 at each Iteration, therefore the number 495 is known as Kaprekar Constant.

Steps to Follow

  1. Take any three-digit number with different digits.
  2. Form the highest number and lowest number from this three-digit number.
  3. Find the difference using subtraction method, and the end-result will be 495 [First Iteration].
  4. If the end-result is other than 495 in Step 3, then again follow the process from Steps 1 – 3. But in this case, three-digit number to consider will be the result obtained in Step 3.
  5. Form the highest number and lowest number from this three-digit number.
  6. Find the difference using subtraction method, and the end-result will be 495 [Second Iteration].
  7. If the end-result is other than 495 in Step 6, then again follow the process from Steps 1 – 3. But in this case, three-digit number to consider will be the result obtained in Step 6.
  8. Form the highest number and lowest number from this three-digit number.
  9. Find the difference using subtraction method, and the end-result will be 495 [Third Iteration].
  10. If the end-result is other than 495 in Step 9, then again follow the process from Steps 1 – 3. But in this case, three-digit number to consider will be the result obtained in Step 9.
  11. Form the highest number and lowest number from this three-digit number.
  12. Find the difference using subtraction method, and the end-result will be 495 [Fourth Iteration].
  13. If the end-result is other than 495 in Step 12, then again follow the process from Steps 1 – 3. But in this case, three-digit number to consider will be the result obtained in Step 12.
  14. Form the highest number and lowest number from this three-digit number.
  15. Find the difference using subtraction method, and the end-result will be 495 [Fifth Iteration].
  16. If the end-result is other than 495 in Step 15, then again follow the process from Steps 1 – 3. But in this case, three-digit number to consider will be the result obtained in Step 15.
  17. Form the highest number and lowest number from this three-digit number.
  18. Find the difference using subtraction method, and the end-result will be 495 [Sixth Iteration].
  19. If the end-result is other than 495 in Step 18, then again follow the process from Steps 1 – 3. But in this case, three-digit number to consider will be the result obtained in Step 18.
  20. Form the highest number and lowest number from this three-digit number.
  21. Find the difference using subtraction method, and the end-result will be 495 [Seventh Iteration]. Repeat this process if the end-result is other than the number 495.

Note

Kaprekar Constant fits for any three-digit number excluding 111, 222, 333, 444, 555, 666, 777, 888, 999.

Example

  1. Take three-digit number 123.
  2. Highest and lowest numbers formed from this three-digit number are 321 and 123, respectively.
  3. Difference after subtraction method (321 – 123) is 198 [First Iteration].
  4. The end-result in Step 3 is other than 495, so follow the process from Steps 1 – 3. In this case, three-digit number to consider is 198.
  5. Highest and lowest numbers formed from this three-digit number are 891 and 189, respectively.
  6. Difference after subtraction method (891 – 189) is 702 [Second Iteration].
  7. The end-result in Step 6 is other than 495, so follow the process from Steps 1 – 3. In this case, three-digit number to consider is 702.
  8. Highest and lowest numbers formed from this three-digit number are 720 and 027, respectively.
  9. Difference after subtraction method (720 – 027) is 693 [Third Iteration].
  10. The end-result in Step 9 is other than 495, so follow the process from Steps 1 – 3. In this case, three-digit number to consider is 693.
  11. Highest and lowest numbers formed from this three-digit number are 963 and 369, respectively.
  12. Difference after subtraction method (963 – 369) is 594 [Fourth Iteration].
  13. The end-result in Step 12 is other than 495, so follow the process from Steps 1 – 3. In this case, three-digit number to consider is 594.
  14. Highest and lowest numbers formed from this three-digit number are 954 and 459, respectively.
  15. Difference after subtraction method (954 – 459) is 495 [Fifth Iteration].

In this example, the end-result 495 has been obtained in Fifth Iteration.

Hope you have understood the above-mentioned steps along with this example. You can try yourself using any other three-digit number. In case of any issue, kindly provide your valuable comments.

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