**6174**is known as

**Kaprekar's constant**

^{[1]}

^{[2]}

^{[3]}after the Indian mathematician D. R. Kaprekar. This number is notable for the following property:

- Take any four-digit number, using at least two different digits. (Leading zeros are allowed.)
- Arrange the digits in ascending and then in descending order to get two four-digit numbers, adding leading zeros if necessary.
- Subtract the smaller number from the bigger number.
- Go back to step 2.

**Kaprekar's routine**, will always reach 6174 in at most 7 iterations.

^{[4]}Once 6174 is reached, the process will continue yielding 7641 – 1467 = 6174. For example, choose 3524:

- 5432 – 2345 = 3087
- 8730 – 0378 = 8352
- 8532 – 2358 =
**6174**

- 2111 – 1112 = 0999
- 9990 – 0999 = 8991 (rather than 999 – 999 = 0)
- 9981 – 1899 = 8082
- 8820 – 0288 = 8532
- 8532 – 2358 =
**6174**

- 9831 – 1389 = 8442
- 8442 – 2448 = 5994
- 9954 – 4599 = 5355
- 5553 – 3555 = 1998
- 9981 – 1899 = 8082
- 8820 – 0288 = 8532 (rather than 882 – 288 = 594)
- 8532 – 2358 =
**6174**

495 is the equivalent constant for three-digit numbers. For five-digit numbers and above, there is no single equivalent constant; for each digit length the routine may terminate at one of several fixed values or may enter one of several loops instead.

^{[4]}

## See also

## References

**^**Mysterious number 6174**^**Kaprekar DR (1955). "An Interesting Property of the Number 6174".*Scripta Mathematica***15**: 244–245.**^**Kaprekar DR (1980). "On Kaprekar Numbers".*Journal of Recreational Mathematics***13**(2): 81–82.- ^
^{a}^{b}Weisstein, Eric W., "Kaprekar Routine" from MathWorld.

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