Number analysis
1
The multiplicative identity. Neither prime nor composite — excluding it is what makes prime factorisation unique.
The multiplicative identity. Neither prime nor composite — excluding it is what makes prime factorisation unique.
The number itself
- Value
- 1
- Digits
- 1
- Digit sum
- 1
- Reversed
- 1
- Palindrome
- Yes
1
Digit sum repeated until one digit remains; equals n mod 9 (with 9 for multiples of 9).
Reads the same in both directions.
Parity and primality
- Parity
- Odd
- Primality
- Unit
- Nearest primes
- — ← → 2
Leaves remainder 1 on division by 2.
One is neither prime nor composite. Excluding it is what makes prime factorisation unique.
Divisors
- Aliquot sum
- 0
- Classification
- Deficient
1
The proper divisors — everything except n itself.
Its proper divisors fall short by 1.
How many integers from 1 to n share no factor with n.
Sums and additive structure
- Sum of two squares
- Yes
- Sum of three squares
- Yes
- Sum of four squares
- Yes
- Sum of two cubes
- 0³ + 1³
0² + 1² = 1
Legendre's three-square theorem allows it.
Lagrange's four-square theorem: every non-negative integer is, without exception.
Shapes and sequences
- Triangular number
- Yes — the 1st
- Square number
- Yes — the 1st
- Pentagonal number
- Yes — the 1st
- Hexagonal number
- Yes — the 1st
- Perfect cube
- Yes — 1³
- Fibonacci number
- Yes — index 1
- Catalan number
- Yes — index 0
- Power of two
- Yes — 2^0
Digit curiosities
- Happy number
- Yes
- Armstrong number
- Yes, trivially
- Harshad number
- Yes
- Automorphic
- Yes
- Kaprekar number
- Yes
- Collatz trajectory
- 0 steps to 1
Repeatedly summing the squares of its digits reaches 1.
Every single-digit number equals itself raised to the first power, so all ten qualify trivially.
Divisible by its digit sum 1 — 1 ÷ 1 = 1.
Its square 1 ends in 1.
Peaks at 1 along the way.
Written other ways
- Binary
- 1
- Octal
- 1
- Base 36
- 1
- In words
- one
- Scientific notation
- 1 × 10^0
Is 1 a prime number?
One is neither prime nor composite. Excluding it is what makes prime factorisation unique.
Nearby numbers
Other numeral systems
Beyond the bases and Roman numerals above, these notations write 1 their own way.
- Greek (alphabetic)
- Αʹ
- Babylonian cuneiform
- 𒐕
- Tamil
- ௧
References
Further reading: Wikipedia · MathWorld · 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.