Numberwise

6,174

6174 is Kaprekar's constant: almost every four-digit number reaches it within seven steps of a simple repeated operation.

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Where 6,174 fits

Where 6,174 fits: Mathematics, Related numbersMathematics: Harshad (Niven) number. Related numbers: 495.MathematicsHarshad (Niven) numberRelated numbers4956,174
6,174 connects to 2 worlds: mathematics, related numbers.

Why 6,174 is special

6174 is a fixed point that is easy to test yourself. Take any four-digit number with at least two different digits, arrange the digits in descending then ascending order, and subtract the smaller from the larger. Repeat. Every such number reaches 6174 in at most seven iterations, and 6174 maps to itself: 7641 − 1467 = 6174. The result was described by D. R. Kaprekar in 1949.

Factors & digit properties

Divisors (24)
1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 49, 63, 98, 126, 147, 294, 343, 441, 686, 882, 1029, 2058, 3087, 6174
Prime factorisation
2 × 3^2 × 7^3
Digit sum
18
Digital root
9

Representations

Decimal
6174
Binary
1100000011110
Octal
14036
Hexadecimal
181e
Scientific notation
6.174 × 10^3

Other mathematical patterns

  • Abundant number
  • Harshad (Niven) number

Related numbers & connections

Shared classification
Kaprekar's constants for three and four digits. The same rearrange-and-subtract routine converges on 495 from any three-digit start and on 6,174 from any four-digit one.

Kaprekar's constants for three and four digits. The same rearrange-and-subtract routine converges on 495 from any three-digit start and on 6,174 from any four-digit one.

View 495

Shares a distinctive class

  • is associated with495
    why?

    Strength 0.50, confidence "high".

How is 6,174 connected to another number? →

Mathematics

  • Kaprekar's routine is one of the few named results a reader can verify unaided in a couple of minutes. Order the digits of any four-digit number downwards, order them upwards, subtract, and repeat with the answer; whatever you start from, provided the digits are not all identical, you land on 6174 within seven rounds and stay there. Because there are only 10,000 possible starting points, the claim has been checked exhaustively rather than argued.

    DocumentedMathematicsPeriod: 1949

Common questions

Is 6,174 a prime number?

No, 6,174 is not prime.

What are the factors of 6,174?

The factors of 6,174 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 49, 63, 98, 126, 147, 294, 343, 441, 686, 882, 1029, 2058, 3087, 6174.

About this page's data

Mathematical facts:computed directly from the number's value — nothing to source or verify externally.

Contextual records: 1 reviewer-confirmed record, sourced and reviewed before publication.

Last reviewed: 3 August 2026