36 (number)

← 35 36 37 →
←30313233343536373839→ List of numbers Integers ←0102030405060708090→
Cardinal	thirty-six
Ordinal	36th (thirty-sixth)
Factorization	22× 32
Divisors	1, 2, 3, 4, 6, 9, 12, 18, 36
Greek numeral	ΛϚ´
Roman numeral	XXXVI
Binary	1001002
Ternary	11003
Senary	1006
Octal	448
Duodecimal	3012
Hexadecimal	2416

36(thirty-six) is thenatural numberfollowing35and preceding37.

In mathematics

36 depicted as a triangular number and as a square number

36 as the sum of the first positive cubes

36 is both thesquareofsix,and the eighthtriangular numberor the sum of the first eight non-zero positiveintegers,which makes 36 the first non-trivialsquare triangular number.Aside from being the smallest square triangular number other than1,it is also the only triangular number (other than 1) whosesquare rootis also a triangular number. 36 is also the eighthrefactorable number,as it has exactly nine positive divisors, and9is one of them;in fact, it is the smallest positive integer with at least ninedivisors,which leads 36 to be the 7thhighly composite number.It is the sum of the fourth pair oftwin-primes(17+19),and the 18thHarshad numberindecimal,as it is divisible by the sum of its digits (9).

It is the smallest number$n$with exactly eight solutions (37,57,63,74,76,108,114,126) to theEuler totient function$\phi (x)=n$.Adding up some subsets of its divisors (e.g., 6, 12, and 18) gives 36; hence, it is also the eighthsemiperfect number.

This number is the sum of the cubes of the first three positiveintegersand also the product of the squares of the first three positive integers.

36 is the number of degrees in theinterior angleof each tip of a regularpentagram.

Thethirty-six officers problemis amathematical puzzlewith no solution.

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

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

Thetruncated cubeand thetruncated octahedronareArchimedean solidswith 36 edges.

The number ofdomino tilingsof a 4×4checkerboardis 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 anErdős–Woods number.

The sum of the integers from 1 to 36 is666(seenumber of the beast).

36 is also aTridecagonalnumber.

Measurements

• The number of inches in a yard (3 feet).
• In the UK, a standard beerbarrelis 36 UK gallons, about 163.7 litres.
• threedozen,or a quarter of agross.

In science

• Theatomic numberofkrypton
• Many early computers featured a36-bitword length
• 36 is the number of characters required to store the display name of aUUIDorGUID(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 theMidrash,the light created by God on the first day ofcreationshone for exactly 36 hours; it was replaced by the light of theSunthat was created on the Fourth Day.TheTorahcommands 36 times to love, respect and protect the stranger.Furthermore, in every generation there are 36righteous people(the"Lamed Vav Tzadikim") in whose merit the world continues to exist.In the modern celebration ofHanukkah,36 candles are kindled in the menorah over the eight days of that holiday (not including theshamashcandle).
• In oneMāorilegend, concerning the creation of mankind by the godTāne,36 gods took active part in assembling the various parts of the first human before Tāne breathed life into her.
• InShaivism(s.a.Kaśmir Śaivism),The 36 tattvasdescribe the Absolute, its internal aspects and the creation including living beings, down to the physical reality.
• In Egyptian religion, the 36decansare a series of gods presiding over the degrees of the zodiac and the fixed stars.
• TraditionalHindumarriage bases compatibility on a set of 36 astrological qualities orGunas,18 of which must be shared if the union is to be considered auspicious.

In the arts, culture, and philosophy

• 36 Views of Mount Fuji,a famous series of prints by Japanese ukiyo-e artist Katsushika Hokusai
• The 36th Chamber of Shaolinis a 1978 kung fu film
• 36 Quai des Orfèvres,often referred to simply as36,a French police film
• The Thirty-Six Dramatic Situationsare considered a useful conceptual aid in theater.
• Thirty-Six Stratagemsare a collection of Chinese proverbs illustrating useful approaches to conflict situations.
• In French-speaking countries, 36 is often used as aplaceholder number.
• 36 Crazyfistsare 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 byWu-Tang Clan
• The 36 Lessons of Vivecis the title of a book series in the video gameThe 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 song bySystem of a Down
• "36 Degrees"is a song by the band Placebo

In sports

• Most runs one can hit off a (non-penalised) over in cricket. Seesix sixes in an over.
• The amount of races in aNASCAR Cup Seriesseason.
• Australian basketball team theAdelaide 36ersis named after the year in whichSouth Australiawas founded.
• The number of consecutive bowling strikes in a 900 series (3 consecutive perfect games)
• The number of vehicles that run in each race ofNASCAR'sCamping World Truck Series.

In other fields

• Perfect score on theACT.
• (Oilfield terminology): Apipe wrench36 inches long
• +36is the code for international direct-dialphone calls toHungary

See also

• List of highways numbered 36