Number analysis
21
21 is a composite odd number that factors as 3 × 7.
21 is a composite odd number that factors as 3 × 7.
The number itself
- Value
- 21
- Digits
- 2
- Digit sum
- 3
- Reversed
- 12
- Palindrome
- No
2 + 1
Digit sum repeated until one digit remains; equals n mod 9 (with 9 for multiples of 9).
Reverses to 12.
Parity and primality
- Parity
- Odd
- Prime
- No
- Prime factorisation
- 3 × 7
- Squarefree
- Yes
- Semiprime
- Yes
- Möbius μ(n)
- 1
- Nearest primes
- 19 ← → 23
Leaves remainder 1 on division by 2.
Composite — it factors as 3 × 7.
2 distinct prime factors, 2 with multiplicity.
No prime divides it twice.
A product of exactly two primes, counted with multiplicity.
(−1) to the power of 2 distinct prime factors.
A gap of 4 between them.
Divisors
- Aliquot sum
- 11
- Classification
- Deficient
1, 3, 7, 21
The proper divisors — everything except n itself.
Its proper divisors fall short by 10.
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
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.
Shapes and sequences
- Triangular number
- Yes — the 6th
- Fibonacci number
- Yes — index 8
Digit curiosities
- Happy number
- No
- Harshad number
- Yes
- Collatz trajectory
- 7 steps to 1
Summing the squares of its digits falls into the 4 → 16 → 37 → … → 4 cycle.
Divisible by its digit sum 3 — 21 ÷ 3 = 7.
Peaks at 64 along the way.
Written other ways
- Binary
- 10101
- Octal
- 25
- Hexadecimal
- 15
- Base 36
- L
- Roman numerals
- XXI
- In words
- twenty-one
- Scientific notation
- 2.1 × 10^1
Is 21 a prime number?
Composite — it factors as 3 × 7.
Nearby numbers
Other numeral systems
Beyond the bases and Roman numerals above, these notations write 21 their own way.
- Greek (alphabetic)
- ΚΑʹ
- Babylonian cuneiform
- 𒎙𒐕
- Tamil
- ௨௰௧
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.