6174 (number)
From Wikipedia, the free encyclopedia
|
|||
| 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]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 would always reach 6174 in at most 7 steps and it stops there. The process stops because 7641 – 1467 = 6174. For example, suppose we choose 5342:
- 5432 – 2345 = 3087
- 8730 – 0378 = 8352
- 8532 – 2358 = 6174
The only four-digit numbers for which this function does not work are repunits 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
