6174 (number)
A method for calculating the constant Kaprekar
To get the Kaprekar - constant of a three -, four -, six-, eight -, nine-or ten-digit decimal number, in which not all digits are the same, you arrange the digits of that number (with leading zeros) once so that the greatest number occurs, and then so that the smallest possible number produced. Then formed by subtracting the difference, and applies the process to the result again. After finitely many steps we obtain - regardless of the initial number - a certain number. This number is called " Kaprekar constant" that after the Indian mathematician DR Kaprekar (1905-1986) was named, who found this property in 1949, first for four -digit numbers.
Three-digit Kaprekar constant
The Kaprekar constant for three-digit numbers is always 495 Example:
Output number:
Four-digit Kaprekar constant
The Kaprekar constant for four -digit numbers is always 6174 example.:
Output number:
Other examples
- For two -, five - and seven -digit numbers, there is no Kaprekar constants. For two-digit numbers, the method described leads to the following cycle: 9 → 81 → 63 → 27 → 45 → 9
- For six -, eight - and nine-digit there are two Kaprekar constants that alternatively be achieved with the method described: for six digit numbers: 549945, 631 764
- For eight-digit numbers: 63317664, 97508421
- For nine digit numbers: 554999445, 864197532