What is Kaprekar's constant?

What is Kaprekar's constant?

Image credit: en.wikipedia.org

Who is Kaprekar?

  Dattathreya Ramchandra Kaprekar was an Indian recreational mathematician. Working alone without graduation in maths, he made great discoveries. Kaprekar's constant is one of it named after him.

What is Kaprekar's constant?

  In the year 1949, Kaprekar discovered an interesting property of the number 6174. This number is known for the following property:

1. Take any four digit number using at least two different digits.
2. Arrange the digits in ascending and descending order to get two four digit numbers, adding leading zeros if necessary.
3. Subtract the smaller number from the greater one.
4. Go back to step 2 and repeat.

  The above process, known as Kaprekar's routine, will usually reach its fixed point 6174 at the last iteration. Once 6174 is reached, the process will continue because 7641-1467=6174.

  Kaprekar also found out the same property number for three digit numbers. It was 495.

What are repdigits?

  Four digit numbers that do not reach 6174 after Kaprekar's routine are known as repdigits such as 1111, 2222, etcetera.

What is an example of Kaprekar's constant?

  For better understanding of the Kaprekar's constant, let's take an example:

Number taken:1234

4321-1234=3087

8730-0378=8352

8532-2358=6174

7641-1467=6174

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