Tool using the Kaprekar algorithm. It uses an integer N, and arranges its digits in ascending and descending order, before subtracting them.

Kaprekar Algorithm - dCode

Tag(s) : Mathematics, Algorithm

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Tool using the Kaprekar algorithm. It uses an integer N, and arranges its digits in ascending and descending order, before subtracting them.

Kaprepar routine consists in forming integers N1, respectively N2, by arranging digits in ascending, respectively descending order. It forms then N = N2-N1 and repeat the process until a previous number is found.

Example: N = 7533, N1 = 3357, N2=7533, one replace N by 7533-3357=4176

N = 4176, N1 = 1467, N2=7641, one replace N by 7641-1467=6174

N = 6174, N1 = 1467, N2=7641, one replace N by N=7641-1467=6174, there is a loop on constant 6174, called Kaprekar Constant.

Loops are repetition of values or constants that appears in the algorithm.

Number of digits | Constant/Loop |
---|---|

3 | 495 |

4 | 6174 |

5 | 53955, 59994 or 62964, 71973, 83952, 74943 or 61974, 82962, 75933, 63954 |

6 | 420876, 851742, 750843, 840852, 860832, 862632, 642654 or 631764 or 549945 |

7 | 7509843, 9529641, 8719722, 8649432, 7519743, 8429652, 7619733, 8439552 |

8 | 43208766, 85317642, 75308643, 84308652, 86308632, 86326632, 64326654 or 64308654, 83208762, 86526432 or 97508421 or 63317664 |

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