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Factorization22 × 32
Divisors1, 2, 3, 4, 6, 9, 12, 18, 36
Greek numeralΛϚ´
Roman numeralXXXVI

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

In mathematics[edit]

36 depicted as a triangular number and as a square number

36 is both the square of six, and the eighth triangular number[1] or sum of the first eight non-zero positive integers, which makes 36 the first non-trivial square triangular number.[2] Aside from being the smallest square triangular number other than thở 1, it is also the only triangular number (other than thở 1) whose square root is also a triangular number. 36 is also the eighth refactorable number, as it has exactly nine positive divisors, and 9 is one of them;[3] in fact, it is the smallest number with exactly nine divisors, which leads 36 to lớn be the 7th highly composite number.[4] It is the sum of the fourth pair of twin-primes (17 + 19),[5] and the 18th Harshad number in decimal, as it is divisible by the sum of its digits (9).[6]

It is the smallest number with exactly eight solutions (37, 57, 63, 74, 76, 108, 114, 126) to lớn the Euler totient function . Adding up some subsets of its divisors (e.g., 6, 12, and 18) gives 36; hence, it is also the eighth semiperfect number.[7]

This number is 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 with no solution.[8]

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

36 is the largest numeric base that some computer systems tư vấn 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.[9]

The number of domino tilings of a 4×4 checkerboard is 36.[10]

Since it is possible to lớn find sequences of 36 consecutive integers such that each inner thành viên shares a factor with either the first or the last thành viên, 36 is an Erdős–Woods number.[11]

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

  • 36 is equal to lớn the Sum of its Non-Prime Power Factors, excluding even 1 = prime^0 and Itself.

So, it's a Non-Prime Power Factor Multiply Perfect Number. Other such numbers include 392, 30752, 40440, 111644, etc.

36 has Non-Prime Power Factors = 6, 12, 18

Sum of Non-Prime Power Factors = 6 + 12 + 18 = 36

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  • The number of inches in a yard (3 feet).[12]
  • In the UK, a standard beer barrel is 36 UK gallons, about 163.7 litres.[12]
  • 3 dozen, or a quarter of a gross.

In science[edit]

  • The atomic number of krypton[13]
  • Many early computers featured a 36-bit word length[14]
  • 36 is the number of characters required to lớn store the display name of a UUID or GUID (e.g., 00000000-0000-0000-C000-000000000046).

In religion[edit]

  • Jewish tradition holds that the number 36 has had special significance since the beginning of time: According to lớn 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.[15] The Torah commands 36 times to lớn love, respect and protect the stranger.[15] Furthermore, in every generation there are 36 righteous people (the "Lamed Vav Tzadikim") in whose merit the world continues to lớn exist.[15] In the modern celebration of Hanukkah, 36 candles are kindled in the menorah over the eight days of that holiday (not including the shamash candle).[15]
  • 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.[16]
  • In Shaivism (s.a. Kaśmir Śaivism), The 36 tattvas describe the Absolute, its internal aspects and the creation including living beings, down to lớn the physical reality.
  • In Egyptian religion, the 36 decans are a series of gods presiding over the degrees of the zodiac and the fixed stars.[17]

In the arts, culture, and philosophy[edit]

  • 36 Views of Mount Fuji, a famous series of prints 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 lớn simply as 36, a French police film
  • The Thirty-Six Dramatic Situations are considered a useful conceptual aid in theater.
  • Thirty-Six Stratagems are a collection of Chinese proverbs illustrating useful approaches to lớn 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 is the alias of 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 clip game The Elder Scrolls III: Morrowind.
  • The game of roulette has 36 numbers on the number layout 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" is a tuy nhiên by System of a Down
  • "36 Degrees" is a tuy nhiên by the band Placebo

In sports[edit]

  • Most runs one can hit off a (non-penalised) over in cricket. See six sixes in an over.[citation needed]
  • The amount of races in a NASCAR Cup Series season.
  • Australian basketball team the Adelaide 36ers is named after the year in which South nước Australia was founded.[18]
  • The number of consecutive bowling strikes in a 900 series (3 consecutive perfect games)
  • The number of vehicles that run rẩy in each race of NASCAR's Camping World Truck Series.
  • India's lowest ever test innings score in cricket, versus nước Australia at the Adelaide Oval on 18 December 2020

In other fields[edit]

  • Perfect score on the ACT.
  • (Oilfield terminology): A pipe wrench 36 inches long
  • +36 is the code for international direct-dialphone calls to lớn Hungary

See also[edit]

  • List of highways numbered 36


  1. ^ Sloane, N. J. A. (ed.). "Sequence A000217 (Triangular numbers.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-06-15.
  2. ^ "Sloane's A001110 : Square triangular numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
  3. ^ Sloane, N. J. A. (ed.). "Sequence A033950 (Refactorable numbers: number of divisors of k divides k. Also known as tau numbers.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-06-15.
  4. ^ "Sloane's A002182 : Highly composite numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
  5. ^ Sloane, N. J. A. (ed.). "Sequence A001097 (Twin primes.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-06-15.
  6. ^ Sloane, N. J. A. (ed.). "Sequence A005349 (Niven (or Harshad, or harshad) numbers: numbers that are divisible by the sum of their digits.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-06-15.
  7. ^ "Sloane's A005835 : Pseudoperfect (or semiperfect) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
  8. ^ Weisstein, Eric W. "36 Officer Problem". mathworld.wolfram.com. Retrieved 2020-08-21.
  9. ^ Weisstein, Eric W. "Archimedean Solid". mathworld.wolfram.com. Retrieved 2020-08-21.
  10. ^ Weisstein, Eric W. "Domino Tiling". mathworld.wolfram.com. Retrieved 2020-08-21.
  11. ^ "Sloane's A059756 : Erdős-Woods numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
  12. ^ a b "How Many? A Dictionary of Units of Measurement. -Y". Archived from the original on 22 September 2007. Retrieved 2007-09-15.
  13. ^ "WebElements.com – Krypton". Archived from the original on 4 August 2007. Retrieved 2007-08-13.
  14. ^ "36bit.org". Archived from the original on 11 September 2007. Retrieved 2007-09-15.
  15. ^ a b c d Winston, Pinchas (1995). The Wonderful World of Thirty-six. Mercava Productions. ISBN 0-9698032-4-9.
  16. ^ "The Creation of Man". The Coming of the Maori. Retrieved 2016-04-24.
  17. ^ Betz, Hans Dieter (1996). The Greek Magical Papyri in Translation. ISBN 9780226044477.
  18. ^ "Adelaide 36ers Homepage". Archived from the original on 11 August 2007. Retrieved 13 August 2007.