36 (number)

36 is the natural number following 35 and preceding 37.

Cardinal	thirty-six
Ordinal	36th (thirty-sixth)
Factorization
Divisors	2, 3, 4, 6, 9, 12, 18
Roman numeral	XXXVI
Binary	100100
Hexadecimal	24

In mathematics

It is the square of 6 as well as a triangular number, making it a triangular square number. It is also a 13-gonal number and a highly composite number. It is a Harshad 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 smallest number n with exactly 8 solutions to the equation φ(x) = n.

36 is the largest base Mathematica's BaseForm command can handle since it represents base 36 numbers with the numerals 0 - 9 and the letters A - Z.

In science

• The atomic number of krypton

In 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

The Saros number of the solar eclipse series which began on -1859 June 23 and ended on -561 August 11. The duration of Saros series 36 was 1298.1 years, and it contained 73 solar eclipses.

The Saros number of the lunar eclipse series which began on -1521 April 24 and ended on -223 June 11. The duration of Saros series 36 was 1298.1 years, and it contained 73 lunar eclipses.

In other fields

Thirty-six is also:

• On the piano, the number of black keys (for notes not on the C major scale).
• The code for direct dial international phone calls to Hungary.
• In the title of the movie 36 Fillette, starring Delphine Zentout and Oliver Parniere , directed by Catherine Breillat
• The Thirty-Six Strategies is a Chinese collection of 36 proverbs commented as militaristic tactics.
• Historical years: 36 A.D., 36 B.C., or 1936