Kaprekar routine: take any 4-digit number (not all same digit), sort desc − sort asc, repeat. Always reaches 6174 in ≤ 7 steps! Example: 3524→5432−2345=3087→8730−0378=8352→8532−2358=6174. For 3 digits: reaches 495. For 2: cycle.
How to Use
Enter number:
- Steps: Full iteration
- Constant: Fixed point
- Cycle: For non-converging cases
Kaprekar Constants
2 digits: cycle 9→81→63→27→45→9. 3 digits: 495. 4 digits: 6174. 5 digits: no single constant (three cycles). 6 digits: 549945, 631764. The behavior depends on digit count.
Why 6174?
D.R. Kaprekar discovered in 1949 that 6174 is a fixed point: 7641−1467=6174. It can be proven by exhaustive analysis of all 4-digit numbers that all paths lead to 6174 within 7 steps.
Step-by-Step Instructions
- 1Enter number.
- 2Watch iteration.
- 3Count steps.
- 4Reach constant.
- 5Try other sizes.