81 (number)

81 (eighty-one) is the natural number following 80 and preceding 82.

← 80 82 → 81
← 80 81 82 83 84 85 86 87 88 89 → List of numbers — Integers 0 10 20 30 40 50 60 70 80 90 →
Cardinal	eighty-first
Ordinal	81st (eighty-first)
Numeral system	81
Factorization	34
Divisors	1, 3, 9, 27, 81
Roman numeral	LXXXI
Binary	10100012
Octal	1218
Duodecimal	6912
Hexadecimal	5116

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

• Messier object M81, a magnitude 8.5 spiral galaxy in the constellation Ursa Major, also known as Bode's Galaxy, and the first of what is known as the M81 Group of galaxies
• The New General Catalogue object NGC 81, a spiral galaxy in the constellation Andromeda
• The Saros number of the solar eclipse series which began on -322 May 12 and ended on 958 June. The duration of Saros series 81 was 1280.1 years, and it contained 72 solar eclipses. Further, the number of lunar eclipse series which began on -20 February 19 and ended on 1296 April. The duration of Saros series 81 was 1316.2 years, and it contained 74 lunar eclipses.

In other fields

Eighty-one is also:

• The number of squares on a shogi playing board
• The year AD 81, 81 BC, or 1981.
• The atomic number of thallium
• The symbolic number of the Hells Angels Motorcycle Club. 'H' and 'A' are the 8th and 1st letter of the alphabet, respectively.
• The title of a short film by Stephen Burke: 81
• The model number of Sinclair ZX81
• The number of the department in France called Tarn
  

  

  Department 81 of France (Tarn)
• The designation of Interstate 81, a freeway that runs from Tennessee to New York.
• The code for international direct dial phone calls to Japan
• One of two ISBN Group Identifiers for books published in India
• Number of stanzas or chapters in the Tao te Ching (in the most common arrangements).
• Number of provinces in Turkey. 81st one is Düzce.
• Number of prayers said in the Rosary in each night.
• The 81 is a 1965 song by Candy and the Kisses.
• Artemis 81 is a 1981 BBC TV sci-fi drama.
• 'The Eighty-One Brothers' is a Japanese fable

81 was the number worn by James Amato of the Flying Hellfish flag football team

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.