Number analysis
2,048
2,048 is a composite even number that factors as 2^11.
2,048 is a composite even number that factors as 2^11.
The number itself
- Value
- 2,048
- Digits
- 4
- Digit sum
- 14
- Reversed
- 8,402
- Palindrome
- No
2 + 0 + 4 + 8
Digit sum repeated until one digit remains; equals n mod 9 (with 9 for multiples of 9).
Reverses to 8,402.
Parity and primality
- Parity
- Even
- Prime
- No
- Prime factorisation
- 2^11
- Squarefree
- No
- Prime power
- 2^11
- Powerful
- Yes
- Möbius μ(n)
- 0
- Nearest primes
- 2,039 ← → 2,053
Divisible by 2.
Composite — it factors as 2^11.
1 distinct prime factor, 11 with multiplicity.
At least one prime appears squared.
A single prime raised to a power.
Every prime factor appears at least squared.
Zero, because a squared prime divides n.
A gap of 14 between them.
Divisors
- Sum of divisors σ(n)
- 4,095
- Aliquot sum
- 2,047
- Classification
- Deficient
- Euler totient φ(n)
- 1,024
1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1,024, 2,048
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
- Goldbach pair
- 19 + 2,029
32² + 32² = 2,048
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
- Power of two
- Yes — 2^11
Digit curiosities
- Happy number
- No
- Harshad number
- No
- Collatz trajectory
- 11 steps to 1
Summing the squares of its digits falls into the 4 → 16 → 37 → … → 4 cycle.
Not divisible by its digit sum 14.
Peaks at 2,048 along the way.
Written other ways
- Binary
- 100000000000
- Octal
- 4000
- Hexadecimal
- 800
- Base 36
- 1KW
- Roman numerals
- MMXLVIII
- In words
- two thousand and forty-eight
- Scientific notation
- 2.048 × 10^3
Is 2,048 a prime number?
Composite — it factors as 2^11.
Nearby numbers
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.