Number analysis
13
The subject of triskaidekaphobia; many buildings omit a 13th floor.
The subject of triskaidekaphobia; many buildings omit a 13th floor.
The number itself
- Value
- 13
- Digits
- 2
- Digit sum
- 4
- Reversed
- 31
- Palindrome
- No
1 + 3
Digit sum repeated until one digit remains; equals n mod 9 (with 9 for multiples of 9).
Reverses to 31.
Parity and primality
- Parity
- Odd
- Prime
- Yes
- Squarefree
- Yes
- Möbius μ(n)
- -1
- Twin prime
- Yes — paired with 11
- Nearest primes
- 11 ← → 17
Leaves remainder 1 on division by 2.
Divisible only by 1 and itself.
1 distinct prime factor, 1 with multiplicity.
No prime divides it twice.
(−1) to the power of 1 distinct prime factors.
A gap of 6 between them.
Divisors
- Aliquot sum
- 1
- Classification
- Deficient
1, 13
The proper divisors — everything except n itself.
Its proper divisors fall short by 12.
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
2² + 3² = 13
Legendre's three-square theorem allows it.
Lagrange's four-square theorem: every non-negative integer is, without exception.
Shapes and sequences
- Fibonacci number
- Yes — index 7
Digit curiosities
- Happy number
- Yes
- Harshad number
- No
- Collatz trajectory
- 9 steps to 1
Repeatedly summing the squares of its digits reaches 1.
Not divisible by its digit sum 4.
Peaks at 40 along the way.
Written other ways
- Binary
- 1101
- Octal
- 15
- Base 36
- D
- Roman numerals
- XIII
- In words
- thirteen
- Scientific notation
- 1.3 × 10^1
Is 13 a prime number?
Yes. 13 has no divisors other than 1 and itself.
Nearby numbers
Other numeral systems
Beyond the bases and Roman numerals above, these notations write 13 their own way.
- Greek (alphabetic)
- ΙΓʹ
- Babylonian cuneiform
- 𒌋𒐗
- Tamil
- ௰௩
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.