81 (number)

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81
Cardinaleighty-first
Ordinal81st
(eighty-first)
Numeral system81
Factorization3^4
Divisors1, 3, 9, 27, 81
Roman numeralLXXXI
Binary10100012
Ternary100003
Quaternary11014
Octal1218
Duodecimal6912
Hexadecimal5116
Vigesimal4120
Base 362936
 
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81 (eighty-one) is the natural number following 80 and preceding 82.

81
Cardinaleighty-first
Ordinal81st
(eighty-first)
Numeral system81
Factorization3^4
Divisors1, 3, 9, 27, 81
Roman numeralLXXXI
Binary10100012
Ternary100003
Quaternary11014
Octal1218
Duodecimal6912
Hexadecimal5116
Vigesimal4120
Base 362936

Contents

In mathematics

Eighty-one is the square of 9 and the fourth power of 3. Like all powers of three, 81 is a perfect totient number. It is a heptagonal number and a centered octagonal number. It is also a tribonacci number, and an open meandric number. 81 is the ninth member of the Mian-Chowla sequence.

In base 10, it is a Harshad number, and one of three non-trivial numbers (the other two are 1458 and 1729) which, when its digits are added together, produces a sum which, when multiplied by its reversed self, yields the original number:

8 + 1 = 9
9 × 9 = 81

(although this case is somewhat degenerate, as the sum has only a single digit).

The inverse of 81 is 0.012345679 recurring, missing only the digit "8" from the complete set of digits. This is an example of the general rule that, in base b,

\frac{1}{\left(b-1\right)^2} = 0.\overline{012\cdots(b-4)(b-3)(b-1)},

omitting only the digit b−2.

In astronomy

In other fields

Eighty-one is also:

In culture

The Arabic characters for the numerals 8 and 1 are visible in the left palm of the human hand. In China, 81 always reminds people People's Liberation Army as it was founded on August 1.

References