Number analysis
52
52 is a composite even number that factors as 2^2 × 13.
52 is a composite even number that factors as 2^2 × 13.
The number itself
- Value
- 52
- Digits
- 2
- Digit sum
- 7
- Reversed
- 25
- Palindrome
- No
5 + 2
Digit sum repeated until one digit remains; equals n mod 9 (with 9 for multiples of 9).
Reverses to 25.
Parity and primality
- Parity
- Even
- Prime
- No
- Prime factorisation
- 2^2 × 13
- Squarefree
- No
- Möbius μ(n)
- 0
- Nearest primes
- 47 ← → 53
Divisible by 2.
Composite — it factors as 2^2 × 13.
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
- 46
- Classification
- Deficient
1, 2, 4, 13, 26, 52
The proper divisors — everything except n itself.
Its proper divisors fall short by 6.
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
- 5 + 47
4² + 6² = 52
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
- Figurate shapes
- None
Not triangular, square, pentagonal, hexagonal, cubic, Fibonacci, Lucas, Catalan, factorial or a power of two.
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 7.
Peaks at 52 along the way.
Written other ways
- Binary
- 110100
- Octal
- 64
- Hexadecimal
- 34
- Base 36
- 1G
- Roman numerals
- LII
- In words
- fifty-two
- Scientific notation
- 5.2 × 10^1
Is 52 a prime number?
Composite — it factors as 2^2 × 13.
Nearby numbers
Other numeral systems
Beyond the bases and Roman numerals above, these notations write 52 their own way.
- Greek (alphabetic)
- ΝΒʹ
- Babylonian cuneiform
- 𒐐𒐖
- Tamil
- ௫௰௨
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.