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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

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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.

Answers to Questions

How to calculate Kaprekar sequence?

The Kaprekar routine from a number \( N \) consists of creating 2 other numbers \( N_1 \) and \( N_2 \) by arranging the digits of \( N \) in ascending order to \( N_1 \) and decreasing for \( N_2 \). Kaprekar then forms a new number \( N \) such that \( N_2-N_1 = N \) and repeats the process until arriving at a previously found number.

Example: \( N = 7533 \), \( N_1 = 3357 \), \( N_2 = 7533 \), replace \( N \) with \( 7533 - 3357 = 4176 \)
\( N = 4176 \), \( N_1 = 1467 \), \( N_2 = 7641 \) then replace \( N \) with \( 7641 - 1467 = 6174 \)
\( N = 6174 \), \( N_1 = 1467 \), \( N_2 = 7641 \) replace \( N \) with \( 7641 - 1467 = 6174 \), which creates a loop on the constant 6174, called the 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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