81 (number)
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81 is a natural number that comes between 80 and 82. It is a perfect square, being 9 squared, or 9 × 9. It is also the fourth power of 3: 3 × 3 × 3 × 3.
In the decimal number system, 81 is written with two digits: 8 and 1. In mathematics, 81 is a composite number—it can be divided by smaller numbers other than 1 and itself.
Mathematical properties
The divisors of 81 are 1, 3, 9, 27, and 81. All of these are powers of 3, since 81 = 3⁴. For this reason, 81 is a perfect square with square root 9, and also a fourth power with fourth root 3. It is not a perfect cube, since 4 is not divisible by 3.
The sum of the digits of 81 is 8 + 1 = 9, which equals the square root of the number. Numbers whose digit sum equals their own square root form a rare class; 81 is among the smallest with this property.
Number bases
In base 3, 81 is written as 10000, since it is 3⁴ exactly. In binary, it is 1010001. This property makes 81 a useful example for teaching number base conversion.
General use
Standard Sudoku puzzles contain 81 cells arranged in a 9 × 9 grid. In addition, 81 appears as a calendar year, national code, or symbolic number in various systems, with its meaning depending on how it is used.