The above process, known as Kaprekar's routine, will usually reach its fixed point, 6174, in at most 8 iterations. Once 6174 is reached, the process will continue yielding 7641 – 1467 = 6174. For example, choose 3524:
The only four-digit numbers for which Kaprekar's routine does not reach 6174 are repdigits such as 1111, which give the result 0000 after a single iteration. All other four-digit numbers eventually reach 6174 if leading zeros are used to keep the number of digits at 4.
|Cardinal||six thousand one hundred seventy-four|
(six thousand one hundred seventy-fourth)
|Factorization||2 × 32× 73|
Note that there can be analogous fixed points for digit lengths other than four, for instance if we use 3-digit numbers then most sequences (i.e., other than repdigits such as 111) will terminate in the value 495 in at most 6 iterations. Sometimes these numbers (495, 6174, and their counterparts in other digit lengths or in bases other than 10) are called "Kaprekar constants".
6174 is a Harshad number, since it is divisible by the sum of its digits:
6174 is a 7-smooth number, i.e. none of its prime factors are greater than 7.
6174 can be written as the sum of the first three degrees of 18:
18³ + 18² + 18 = 5832 + 324 + 18 = 6174.
The sum of squares of the prime factors of 6174 is a square:
2² + 3² + 3² + 7² + 7² + 7² = 4 + 9 + 9 + 49 + 49 + 49 = 169 = 13².