Kaprekar's Constant (6174)

Run Kaprekar's routine to the fixed point 6174 or 495, and check Kaprekar numbers.

Kaprekar's routine takes a number, arranges its digits from highest to lowest and from lowest to highest, then subtracts the smaller arrangement from the larger one. Repeating this on a four-digit number with at least two different digits always reaches 6174, known as Kaprekar's constant. Three-digit numbers settle on 495 instead.

Example: 3524 → 5432 minus 2345 = 3087 → 8730 minus 0378 = 8352 → 8532 minus 2358 = 6174. Numbers whose digits are all the same, like 1111 or 3333, collapse straight to 0 and have no constant.

Kaprekar's routine

Number

Digit width 4 digits (reaches 6174) 3 digits (reaches 495)

Kaprekar number checker

A Kaprekar number is a number n whose square can be split into a left part and a right part that add up to n. For example 45, because 45² = 2025 and 20 + 25 = 45.

Check a number, or list every Kaprekar number up to it

Listing is limited to 1000000 to stay responsive.