Number analysis
28
The second perfect number, and the length of the lunar month in days to the nearest whole.
The second perfect number, and the length of the lunar month in days to the nearest whole.
The number itself
- Value
- 28
- Digits
- 2
- Digit sum
- 10
- Reversed
- 82
- Palindrome
- No
2 + 8
Digit sum repeated until one digit remains; equals n mod 9 (with 9 for multiples of 9).
Reverses to 82.
Parity and primality
- Parity
- Even
- Prime
- No
- Prime factorisation
- 2^2 × 7
- Squarefree
- No
- Möbius μ(n)
- 0
- Nearest primes
- 23 ← → 29
Divisible by 2.
Composite — it factors as 2^2 × 7.
2 distinct prime factors, 3 with multiplicity.
At least one prime appears squared.
Zero, because a squared prime divides n.
A gap of 6 between them.
Divisors
- Aliquot sum
- 28
- Classification
- Perfect
1, 2, 4, 7, 14, 28
The proper divisors — everything except n itself.
Its proper divisors sum to exactly itself.
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
- No
- Sum of four squares
- Yes
- Sum of two cubes
- 1³ + 3³
- Goldbach pair
- 5 + 23
A prime congruent to 3 mod 4 divides it an odd number of times, which rules it out.
Excluded by Legendre: it has the form 4^a(8b + 7).
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
- Triangular number
- Yes — the 7th
- Hexagonal number
- Yes — the 4th
Digit curiosities
- Happy number
- Yes
- Harshad number
- No
- Collatz trajectory
- 18 steps to 1
Repeatedly summing the squares of its digits reaches 1.
Not divisible by its digit sum 10.
Peaks at 52 along the way.
Written other ways
- Binary
- 11100
- Octal
- 34
- Hexadecimal
- 1C
- Base 36
- S
- Roman numerals
- XXVIII
- In words
- twenty-eight
- Scientific notation
- 2.8 × 10^1
Is 28 a prime number?
Composite — it factors as 2^2 × 7.
Nearby numbers
Other numeral systems
Beyond the bases and Roman numerals above, these notations write 28 their own way.
- Greek (alphabetic)
- ΚΗʹ
- Babylonian cuneiform
- 𒎙𒐜
- Tamil
- ௨௰௮
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.