Analyze my number
Enter any whole number up to 1,000,000,000,000 and see everything computable about it — primality and factorisation, divisors, sums of squares, the shapes and sequences it belongs to, digit curiosities, and how it is written in other notations.
The Hardy–Ramanujan taxicab number: the smallest number expressible as a sum of two cubes in two ways, 1³+12³ and 9³+10³.
The number itself
- Value
- 1,729
- Digits
- 4
- Digit sum
- 19
- Reversed
- 9,271
- Palindrome
- No
1 + 7 + 2 + 9
Digit sum repeated until one digit remains; equals n mod 9 (with 9 for multiples of 9).
Reverses to 9,271.
Parity and primality
- Parity
- Odd
- Prime
- No
- Prime factorisation
- 7 × 13 × 19
- Squarefree
- Yes
- Möbius μ(n)
- -1
- Nearest primes
- 1,723 ← → 1,733
Leaves remainder 1 on division by 2.
Composite — it factors as 7 × 13 × 19.
3 distinct prime factors, 3 with multiplicity.
No prime divides it twice.
(−1) to the power of 3 distinct prime factors.
A gap of 10 between them.
Divisors
- Sum of divisors σ(n)
- 2,240
- Aliquot sum
- 511
- Classification
- Deficient
- Euler totient φ(n)
- 1,296
1, 7, 13, 19, 91, 133, 247, 1,729
The proper divisors — everything except n itself.
Its proper divisors fall short by 1,218.
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
- Sum of two cubes
- 1³ + 12³ · 9³ + 10³
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.
Expressible in 2 distinct ways — a taxicab number, after the Hardy–Ramanujan story about 1729.
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
- 104 steps to 1
Summing the squares of its digits falls into the 4 → 16 → 37 → … → 4 cycle.
Divisible by its digit sum 19 — 1,729 ÷ 19 = 91.
Peaks at 9,232 along the way.
Written other ways
- Binary
- 11011000001
- Octal
- 3301
- Hexadecimal
- 6C1
- Base 36
- 1C1
- Roman numerals
- MDCCXXIX
- In words
- one thousand seven hundred and twenty-nine
- Scientific notation
- 1.729 × 10^3
What gets checked
Everything on this page is computed from the number you enter — nothing is looked up, with the single exception of a short note on a handful of genuinely famous numbers, which only adds context alongside the computed results.
- Primality by deterministic Miller–Rabin, which is exact for every value this page accepts.
- Prime factorisation, plus whether the number is squarefree, powerful, a semiprime or a prime power.
- Divisors: how many, their sum, the aliquot sum, and whether that makes it perfect, abundant or deficient — with the amicable partner if it has one.
- Sums of squares: the Fermat–Euler criterion for two squares with explicit representations, Legendre's rule for three, and Lagrange's guarantee of four.
- Sums of two cubes, flagging taxicab numbers where more than one representation exists.
- Goldbach pairs for even numbers.
- Figurate shapes and sequences: triangular, square, pentagonal, hexagonal, cubic, Fibonacci, Lucas, Catalan, factorial and powers of two, each with its index.
- Digit curiosities: happy, Armstrong, Harshad, automorphic, Kaprekar, palindromic, plus the Collatz trajectory.
- Number-theoretic functions: Euler's totient φ(n) and the Möbius function μ(n).
- Notation: binary, octal, hexadecimal, base 36, Roman numerals, scientific notation and the number spelled out in words.
Limits
The ceiling is 1,000,000,000,000. Factorisation uses trial division, which needs about a million steps at that size — fast enough to feel instant, but a larger bound would not be. Explicit sum-of-two-squares representations are only enumerated below fifty million; above that the page still answers yes or no from the factorisation, and says that it did not list them rather than implying none exist.