Kaprekar Number Checker

n² splits to sum n

CalculatorsFreeNo Signup
4.3(360 reviews)
All Tools

Loading tool...

About Kaprekar Number Checker

A Kaprekar number checker that tests whether n² splits into two parts summing to n. Example: 45² = 2025, 20+25 = 45. Also explores the Kaprekar routine (6174 constant) for 4-digit numbers. All calculations are client-side.

Kaprekar Number Checker Features

  • Kaprekar check
  • Split display
  • 6174 routine
  • Range scan
  • Table
Kaprekar number: n² splits into left+right parts summing to n. Examples: 9 (81→8+1=9), 45 (2025→20+25=45), 297 (88209→88+209=297). The Kaprekar routine: rearrange digits desc−asc, always reaches 6174 for 4-digit numbers.

How to Use

Enter n:

  • Square: n²
  • Split: left + right
  • Sum: Does it equal n?

6174 Routine

Take any 4-digit number (not all digits same). Arrange digits descending − ascending. Repeat. Always reaches 6174 in ≤7 steps. Example: 3524 → 5432−2345 = 3087 → 8730−0378 = 8352 → ... → 6174.

History

Named after D.R. Kaprekar (1905-1986), Indian mathematician who discovered these properties. He was a schoolteacher who made significant contributions to recreational mathematics.

Step-by-Step Instructions

  1. 1Enter n.
  2. 2Check Kaprekar.
  3. 3View split.
  4. 4Try 6174 routine.
  5. 5Scan range.

Kaprekar Number Checker — Frequently Asked Questions

Why is 6174 always reached?+

For any 4-digit number with non-identical digits, the desc−asc operation always converges to 6174. This is 6174's fixed point: 7641−1467 = 6174. The proof involves checking all possible digit combinations, showing each eventually maps to 6174.

Does the 6174 routine work for other digit counts?+

For 3 digits: converges to 495 (954−459=495). For 2 digits: cycles. For 5+ digits: no single fixed point, but there are cycles. The constants 495 and 6174 are unique to their digit counts.

How many Kaprekar numbers exist?+

Kaprekar numbers are infinite but sparse. First few: 1, 9, 45, 55, 99, 297, 703, 999, 2223, 2728, 4879, 4950, 5050, 5292, 7272, 7777, 9999. Every number of the form 10ⁿ−1 (all 9s) is Kaprekar.

More Calculators Tools

Explore all 639 other calculators tools available on Generatr

1-Sample Z-Test Calculator2-Sample Z-Test Calculator3D Surface Area CalculatorA/B Testing Significance CalculatorAbsolute Value CalculatorAbundant Number CheckerAccelerated Aging CalculatorAchromatic Number CalculatorAcyclic Chromatic Number CalculatorAdditive Persistence CalculatorAge CalculatorAging Test CalculatorAlbertson Index CalculatorAlgebraic Connectivity CalculatorAliquot Sequence CalculatorAliquot Sum CalculatorAlternating Series Test CalculatorAmicable Number FinderAnnuity CalculatorAPY CalculatorAquarium CO2 Drop CheckerArea CalculatorArea Under Curve CalculatorArithmetic Sequence CalculatorArmstrong Number CalculatorASCVD Risk CalculatorAspect Ratio CalculatorAtom Bond Connectivity CalculatorAugmented Eccentric Connectivity CalculatorAugmented Zagreb Index Calculator
View all 639 calculators tools
Share this tool: