Number reference
81 explained.
81: eighty-one, composite, perfect square; factors, prime factorization, roots, binary, hexadecimal, and digit properties.
Identity and representations
- Written form
- eighty-one
- Classification
- composite
- Factors
- 1, 3, 9, 27, 81
- Prime factorization
- 3 × 3 × 3 × 3
- Square root
- 9
- Cube root
- 4.326749
- Binary
- 1010001
- Octal
- 121
- Hexadecimal
- 51
- Roman numeral
- LXXXI
- Digit sum
- 9
- Digital root
- 9
What makes 81 notable
- Perfect square. 81 = 9², so a square of side 9 has an area of 81.
81 in everyday use
A sudoku grid has 81 cells, nine rows of nine. Eighty-one is the atomic number of thallium, a toxic metal once used in rat poison and now in some electronics. In Japan, 81 is the international dialling code. In the United States 81 is the number of the interstate that runs from Tennessee to the Canadian border through the Appalachians. A Major League Baseball team plays 81 home games and 81 away games in its 162-game season.
Eighty-one is nine squared and three to the fourth power, and it is the square of its own digit sum, 8 + 1 = 9, a property shared only with 1. Its reciprocal has a famous expansion: 1/81 = 0.012345679012345679…, counting up through the digits but skipping 8. In base 3 it is 10000, and in binary it is 1010001.
Nearby numbers
How to read this page
The factor list shows every way 81 splits into equal whole-number groups — 5 divisors in total. The prime factorisation is the compact form of that same information, and the base conversions restate 81 for contexts that do not use decimal.
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