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Kaprekar Algorithm

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

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Kaprekar Algorithm -

Tag(s) : Mathematics, Algorithm

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# Kaprekar Algorithm

## Calculus through Kaprekar Algorithm

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

### How to calculate Kaprekar sequence?

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.

### What are Kaprekar constants and Kaprekar loops?

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

Number of digitsConstant/Loop
3495
46174
553955, 59994 or 62964, 71973, 83952, 74943 or 61974, 82962, 75933, 63954
6420876, 851742, 750843, 840852, 860832, 862632, 642654 or 631764 or 549945
77509843, 9529641, 8719722, 8649432, 7519743, 8429652, 7619733, 8439552
843208766, 85317642, 75308643, 84308652, 86308632, 86326632, 64326654 or 64308654, 83208762, 86526432 or 97508421 or 63317664

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