Number analysis
12
Highly composite, which is why it survives in clocks, inches and dozens.
Highly composite, which is why it survives in clocks, inches and dozens.
The number itself
- Value
- 12
- Digits
- 2
- Digit sum
- 3
- Reversed
- 21
- Palindrome
- No
1 + 2
Digit sum repeated until one digit remains; equals n mod 9 (with 9 for multiples of 9).
Reverses to 21.
Parity and primality
- Parity
- Even
- Prime
- No
- Prime factorisation
- 2^2 × 3
- Squarefree
- No
- Möbius μ(n)
- 0
- Nearest primes
- 11 ← → 13
Divisible by 2.
Composite — it factors as 2^2 × 3.
2 distinct prime factors, 3 with multiplicity.
At least one prime appears squared.
Zero, because a squared prime divides n.
A gap of 2 between them.
Divisors
- Aliquot sum
- 16
- Classification
- Abundant
1, 2, 3, 4, 6, 12
The proper divisors — everything except n itself.
Its proper divisors overshoot by 4.
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
- 5 + 7
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
- Pentagonal number
- Yes — the 3rd
Digit curiosities
- Happy number
- No
- Harshad number
- Yes
- Collatz trajectory
- 9 steps to 1
Summing the squares of its digits falls into the 4 → 16 → 37 → … → 4 cycle.
Divisible by its digit sum 3 — 12 ÷ 3 = 4.
Peaks at 16 along the way.
Written other ways
- Binary
- 1100
- Octal
- 14
- Base 36
- C
- Roman numerals
- XII
- In words
- twelve
- Scientific notation
- 1.2 × 10^1
Is 12 a prime number?
Composite — it factors as 2^2 × 3.
Nearby numbers
Other numeral systems
Beyond the bases and Roman numerals above, these notations write 12 their own way.
- Greek (alphabetic)
- ΙΒʹ
- Babylonian cuneiform
- 𒌋𒐖
- Tamil
- ௰௨
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.