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36 (number)

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Title: 36 (number)  
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Subject: 37 (number), 35 (number), 6 (number), 30 (number), 33 (number)
Collection: Integers
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36 (number)

35 36 37
Cardinal thirty-six
Ordinal 36th
Factorization 22× 32
Divisors 1, 2, 3, 4, 6, 9, 12, 18, 36
Roman numeral XXXVI
Binary 1001002
Ternary 11003
Quaternary 2104
Quinary 1215
Senary 1006
Octal 448
Duodecimal 3012
Hexadecimal 2416
Vigesimal 1G20
Base 36 1036

36 (thirty-six) is the natural number following 35 and preceding 37.


  • In mathematics 1
  • Measurements 2
  • In science 3
  • In religion 4
  • In the arts, culture, and philosophy 5
  • In sports 6
  • In other fields 7
  • References 8

In mathematics

36 is both the square of 6 and a triangular number, making it a square triangular number. It is the smallest square triangular number other than 1, and it is also the only triangular number other than 1 whose square root is also a triangular number.

It is also a 13-gonal number.

It is the smallest number n with exactly 8 solutions to the equation φ(x) = n. Being the smallest number with exactly 9 divisors, 36 is a highly composite number. Adding up some subsets of its divisors (e.g., 6, 12 and 18) gives 36, hence 36 is a semiperfect number.

This number is the sum of a twin prime (17 + 19), the sum of the cubes of the first three positive integers, and also the product of the squares of the first three positive integers.

36 is the number of degrees in the interior angle of each tip of a regular pentagram.

The thirty-six officers problem is a mathematical puzzle.

The number of possible outcomes (not summed) in the roll of two distinct dice.

36 is the largest numeric base that some computer systems support because it exhausts the numerals, 0-9, and the letters, A-Z. See Base 36.

The truncated cube and the truncated octahedron are Archimedean solids with 36 edges.

In base 10, it is a Harshad number.

The number of domino tilings of a 4×4 checkerboard is 36.

Since it is possible to find sequences of 36 consecutive integers such that each inner member shares a factor with either the first or the last member, 36 is an Erdős–Woods number.

Because 362 + 1 = 1297, a prime, which is larger than 2 × 36, 36 is a Størmer number.

The sum of the integers from 1 to 36 is 666 (see number of the beast).


  • The number of inches in a yard (3 feet).[1]
  • In the UK, a standard beer barrel is 36 UK gallons, about 163.7 litres.[1]

In science

  • 36 is the number of characters required to store the display name of a UUID or GUID (e.g., 00000000-0000-0000-C000-000000000046).

In religion

  • Jewish tradition holds that the number 36 has had special significance since the beginning of time: According to the Midrash, the light created by God on the first day of creation shone for exactly 36 hours; it was replaced by the light of the Sun that was created on the Fourth Day.[4] The Torah commands 36 times to love, respect and protect the stranger.[4] Furthermore, in every generation there are 36 righteous people (the "Lamed Vav Tzadikim") in whose merit the world continues to exist.[4] In the modern celebration of Hanukkah, 36 candles are kindled in the menorah over the 8 days of that holiday (not including the shamash candle).[4]
  • In one Māori legend, concerning the creation of mankind by the god Tāne, 36 gods took active part in assembling the various parts of the first human before Tāne breathed life into her.[5]

In the arts, culture, and philosophy

  • The 36 Views of Mount Fuji, a famous series of prints by Japanese ukiyo-e artist Katsushika Hokusai
  • The The 36 view of the Eiffel Tower, a famous series of prints from Henri Riviere inspired by Japanese ukiyo-e artist Katsushika Hokusai
  • The 36th Chamber of Shaolin is a 1978 kung fu film
  • 36 Quai des Orfèvres, often referred to simply as 36, a French police film
  • The Thirty-Six Dramatic Situations are considered a useful conceptual aid in theater.
  • The Thirty-Six Stratagems are a collection of Chinese proverbs illustrating useful approaches to conflict situations.
  • In French-speaking countries, 36 is often used as a placeholder number.
  • 36 Crazyfists are a four-piece metal band from Alaska.
  • 36? (Thirty-Six) is a Canadian Psychedelic rock band (On Newgrounds)
  • 36 is ambient/experimental musician Dennis Huddleston from the UK.
  • Enter The Wu-Tang (36 Chambers) is an album by Wu-Tang Clan
  • The 36 Lessons of Vivec is the title of a book series in the video game The Elder Scrolls III: Morrowind.
  • The game of roulette has '36' numbers on the playing grid and roulette wheel (together with a '0' or '00' depending on whether it is a European wheel '37' or American wheel '38')
  • The roulette based game Rollorpoker uses ‘36’ playing cards on the wheel and playing grid, instead of numbers.
  • 36 Degrees is a song by the band Placebo

In sports

In other fields


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