36 (number)

← 35 36 37 →
← 30 31 32 33 34 35 36 37 38 39 → List of numbers Integers ← 0 10 20 30 40 50 60 70 80 90 →
Cardinal	thirty-six
Ordinal	th
Factorization	$2^{2}\cdot 3^{2}$
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 the natural number following 35 and preceding 37.

In mathematics

36 is the sum of 1, 2, 3, 4, 5, 6, 7, and 8.

It is the square of 6 as well as a triangular number, making it a square triangular number, and also the only triangular number whose square root is also a triangular number. It is also a 13-gonal number.

36 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), and the sum of the cubes of the first three integers.

36 is the number of degrees in the angle of all 5 tips in a perfect star.

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.

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 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 obviously more than 36 twice, 36 is a Størmer number.

Measurements

• The number of inches in a yard.
• In the UK, a standard beer barrel is 36 UK gallons, about 163.7 litres.
• The number of barleycorns in an English foot.
• The sum of 1+2+3+...+36 is [1]666.

In science

• The atomic number of krypton

• Many early computers featured a 36-bit word length

• ASCII code for the symbol '$'

Astronomy

• Messier object M36, a magnitude 6.5 open cluster in the constellation Auriga

• The New General Catalogue object NGC 36, a spiral galaxy in the constellation Pisces

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. The Torah commands 36 times to love, respect and protect the stranger. Furthermore, in every generation there are 36 righteous people (the "Lamed Vav Tzadikim") in whose merit the world continues to exist. In the modern celebration of Hannukah, 36 candles are kindled in the menorah over the 8 days of that holiday (not including the shamash candle).

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.

In the arts, culture, and philosophy

• 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.
• Perfect score on the ACT.

In sports

• Australian Basketball team The Adelaide 36ers.
• Retired number of former baseball players Robin Roberts of the Phillies and Gaylord Perry of the Giants.
• Retired number of former basketball player Lloyd Neal of the Portland Trail Blazers

Historical years

36 A.D., 36 B.C., 1936, 2036, etc.