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Kaprekar Constant 6174 for Four-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 6174 is called Kaprekar Constant for four-digit number.

Why is the number 6174 called Kaprekar Constant?

In 1949, D. R. Kaprekar discovered an interesting property of the number 6174 through the mathematical calculations.

D. R. Kaprekar observed that when any four-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 6174 either in the first step or in no more than 7 steps.

If the process is continued even after getting the end-result 6174, then the end-result will be always 6174 at each Iteration, therefore the number 6174 is known as Kaprekar Constant.

Steps to Follow

  1. Take any four-digit number with different digits.
  2. Form the highest number and lowest number from this four-digit number.
  3. Find the difference using subtraction method, and the end-result will be 6174 [First Iteration].
  4. If the end-result is other than 6174 in Step 3, then again follow the process from Steps 1 – 3. But in this case, four-digit number to consider will be the result obtained in Step 3.
  5. Form the highest number and lowest number from this four-digit number.
  6. Find the difference using subtraction method, and the end-result will be 6174 [Second Iteration].
  7. If the end-result is other than 6174 in Step 6, then again follow the process from Steps 1 – 3. But in this case, four-digit number to consider will be the result obtained in Step 6.
  8. Form the highest number and lowest number from this four-digit number.
  9. Find the difference using subtraction method, and the end-result will be 6174 [Third Iteration].
  10. If the end-result is other than 6174 in Step 9, then again follow the process from Steps 1 – 3. But in this case, four-digit number to consider will be the result obtained in Step 9.
  11. Form the highest number and lowest number from this four-digit number.
  12. Find the difference using subtraction method, and the end-result will be 6174 [Fourth Iteration].
  13. If the end-result is other than 6174 in Step 12, then again follow the process from Steps 1 – 3. But in this case, four-digit number to consider will be the result obtained in Step 12.
  14. Form the highest number and lowest number from this four-digit number.
  15. Find the difference using subtraction method, and the end-result will be 6174 [Fifth Iteration].
  16. If the end-result is other than 6174 in Step 15, then again follow the process from Steps 1 – 3. But in this case, four-digit number to consider will be the result obtained in Step 15.
  17. Form the highest number and lowest number from this four-digit number.
  18. Find the difference using subtraction method, and the end-result will be 6174 [Sixth Iteration].
  19. If the end-result is other than 6174 in Step 18, then again follow the process from Steps 1 – 3. But in this case, four-digit number to consider will be the result obtained in Step 18.
  20. Form the highest number and lowest number from this four-digit number.
  21. Find the difference using subtraction method, and the end-result will be 6174 [Seventh Iteration].

Note

  1. In maximum 7 iterations, the end-result will be 6174.
  2. Kaprekar Constant fits for any four-digit number excluding 1111, 2222, 3333, 4444, 5555, 6666, 7777, 8888, 9999.

Example

  1. Take four-digit number 1234.
  2. Highest and lowest numbers formed from this four-digit number are 4321 and 1234, respectively.
  3. Difference after subtraction method (4321 – 1234) is 3087 [First Iteration].
  4. The end-result in Step 3 is other than 6174, so follow the process from Steps 1 – 3. In this case, four-digit number to consider is 3087.
  5. Highest and lowest numbers formed from this four-digit number are 8730 and 0378, respectively.
  6. Difference after subtraction method (8730 – 0378) is 8352 [Second Iteration].
  7. The end-result in Step 6 is other than 6174, so follow the process from Steps 1 – 3. In this case, four-digit number to consider is 8352.
  8. Highest and lowest numbers formed from this four-digit number are 8532 and 2358, respectively.
  9. Difference after subtraction method (8532 – 2358) is 6174 [Third Iteration].

In this example, the end-result 6174 has been obtained in Third Iteration.

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

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