Editing Kaprekar's routine (section)

{{Short description|Iterative algorithm}}
In [[number theory]], '''Kaprekar's routine''' is an [[iterative]] algorithm named after its inventor, Indian mathematician [[D. R. Kaprekar]].{{sfn|Kaprekar|1955}}{{sfn|Kaprekar|1980}} Each iteration starts with a four digit [[random number]], sorts the digits into descending and ascending order, and calculates the difference between the two new numbers.

As an example, starting with the number 8991 in [[decimal|base 10]]:
:{{math|1=9981 – 1899 = 8082}}
:{{math|1=8820 – 0288 = 8532}}
:{{math|1=8532 – 2358 = 6174}}
:{{math|1=7641 – 1467 = 6174}}

[[6174 (number)|6174]], known as '''Kaprekar's constant''', is a [[fixed point (mathematics)|fixed point]] of this algorithm. Any four-digit number (in base 10) with at least two distinct digits will reach 6174 within seven iterations.{{sfn|Hanover|2017|loc=Overview|p=1}} The algorithm runs on any [[natural number]] in any given [[number base]].