Number reference
181 explained.
181: one hundred eighty-one, prime, palindromic prime; factors, prime factorization, roots, binary, hexadecimal, and digit properties.
Identity and representations
- Written form
- one hundred eighty-one
- Classification
- prime
- Factors
- 1, 181
- Prime factorization
- 181
- Square root
- 13.453624
- Cube root
- 5.656653
- Binary
- 10110101
- Octal
- 265
- Hexadecimal
- B5
- Roman numeral
- CLXXXI
- Digit sum
- 10
- Digital root
- 1
What makes 181 notable
- Prime. 181 is prime: it has exactly two divisors, 1 and itself, so it cannot be split into equal whole-number groups any other way.
- Palindromic prime. 181 is prime and reads the same forwards and backwards.
181 in everyday use
One hundred eighty-one is a palindromic prime and the larger of the twin primes 179 and 181. It is also a star number: 181 dots can be arranged as a six-pointed star with a hexagonal core, the sixth such figure after 1, 13, 37, 73, and 121. It is a centered square number too, equal to 9² + 10², which is why a 181-piece pattern fits neatly into a square rotated 45 degrees with one dot at the centre.
Because 181 = 9² + 10², the square root of 181 is the length of the diagonal of a 9 by 10 rectangle, and since 181 is a prime of the form 4k + 1 that two-square representation is the only one. It is the 42nd prime, and it is the last palindromic prime before 191. Divide 1 by 181 and the decimal repeats every 180 digits, another full-reptend prime.
Nearby numbers
How to read this page
Because 181 is prime, the factor list stops at 1 and 181 itself, so it cannot be shared into equal whole-number groups. That is also what makes it useful as a building block: every larger number with 181 in its prime factorisation inherits it from here.
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