6174 (number)
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| 6174 | |
|---|---|
| Cardinal | Six thousand one hundred seventy-four |
| Ordinal | Six thousand one hundred seventy-fourth |
| Factorization |  |
| Binary | 1100000011110 |
| Hexadecimal | 181E |
6174 is known as Kaprekar's constant or Kaprekar's Operation[1][2][3] after the Indian mathematician D. R. Kaprekar. This number has an interesting property. Consider the following steps:
- Take any four-digit number (with a few exceptions - see below).
- 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.
The above operation will always reach 6174 in at most 7 steps and it stops there. Once 6174 is reached, the process stops because 7641 – 1467 = 6174. For example, choose 5342:
- 5432 – 2345 = 3087
- 8730 – 0378 = 8352
- 8532 – 2358 = 6174
The only four-digit numbers for which this function does not work are repdigits such as 1111, which give the answer 0 after a single iteration. Numbers with three digits the same, such as 1112, appear to give 999 after one iteration and thus 0 after a second iteration, but work if leading zeros are included:
- 2111 – 1112 = 0999
- 9990 – 0999 = 8991
- 9981 – 1899 = 8082
- 8820 – 0288 = 8532
- 8532 – 2358 = 6174
Patera's constant also has the same property for three-digit numbers.
[edit] External links
[edit] 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.
