Number analysis
6,174
Kaprekar's constant: the reverse-and-subtract routine on any four-digit number with at least two distinct digits reaches 6174 within seven steps.
Kaprekar's constant: the reverse-and-subtract routine on any four-digit number with at least two distinct digits reaches 6174 within seven steps.
The number itself
- Value
- 6,174
- Digits
- 4
- Digit sum
- 18
- Reversed
- 4,716
- Palindrome
- No
6 + 1 + 7 + 4
Digit sum repeated until one digit remains; equals n mod 9 (with 9 for multiples of 9).
Reverses to 4,716.
Parity and primality
- Parity
- Even
- Prime
- No
- Prime factorisation
- 2 × 3^2 × 7^3
- Squarefree
- No
- Möbius μ(n)
- 0
- Nearest primes
- 6,173 ← → 6,197
Divisible by 2.
Composite — it factors as 2 × 3^2 × 7^3.
3 distinct prime factors, 6 with multiplicity.
At least one prime appears squared.
Zero, because a squared prime divides n.
A gap of 24 between them.
Divisors
- Sum of divisors σ(n)
- 15,600
- Aliquot sum
- 9,426
- Classification
- Abundant
- Euler totient φ(n)
- 1,764
1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 49, 63, 98, 126, 147, 294, 343, 441, 686, 882, 1,029, 2,058, 3,087, 6,174
The proper divisors — everything except n itself.
Its proper divisors overshoot by 3,252.
How many integers from 1 to n share no factor with n.
Sums and additive structure
- Sum of two squares
- No
- Sum of three squares
- Yes
- Sum of four squares
- Yes
- Goldbach pair
- 11 + 6,163
A prime congruent to 3 mod 4 divides it an odd number of times, which rules it out.
Legendre's three-square theorem allows it.
Lagrange's four-square theorem: every non-negative integer is, without exception.
The smallest pair of primes summing to n. Goldbach’s conjecture says one always exists; it remains unproven.
Shapes and sequences
- Figurate shapes
- None
Not triangular, square, pentagonal, hexagonal, cubic, Fibonacci, Lucas, Catalan, factorial or a power of two.
Digit curiosities
- Happy number
- No
- Harshad number
- Yes
- Collatz trajectory
- 111 steps to 1
Summing the squares of its digits falls into the 4 → 16 → 37 → … → 4 cycle.
Divisible by its digit sum 18 — 6,174 ÷ 18 = 343.
Peaks at 31,264 along the way.
Written other ways
- Binary
- 1100000011110
- Octal
- 14036
- Hexadecimal
- 181E
- Base 36
- 4RI
- In words
- six thousand one hundred and seventy-four
- Scientific notation
- 6.174 × 10^3
Standard Roman numerals only run from 1 to 3,999.
Is 6,174 a prime number?
Composite — it factors as 2 × 3^2 × 7^3.
Nearby numbers
References
Further reading: Wikipedia · Wikidata
Notations, naming and the links above come from Wikidata, whose structured data is dedicated to the public domain under CC0-1.0. Retrieved 2026-10-07.