216 (number)

← 215 216 217 →
← 200 210 220 230 240 250 260 270 280 290 → List of numbers — Integers ← 0 100 200 300 400 500 600 700 800 900 →
Cardinal	two hundred sixteen
Ordinal	216th (two hundred and sixteenth)
Factorization	2^3× 3^3
Divisors	1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216
Roman numeral	CCXVI
Binary	110110002
Ternary	220003
Quaternary	31204
Quinary	13315
Senary	10006
Octal	3308
Duodecimal	16012
Hexadecimal	D816
Vigesimal	AG20
Base 36	6036

216 (two hundred [and] sixteen) is the natural number following 215 and preceding 217.

Since ${\displaystyle 216=3^{3}+4^{3}+5^{3}=6^{3}}$, it is the smallest cube that is also the sum of three cubes (Plato was among the first to notice this, and mentioned it in Book VIII of Republic). It is also the sum of a twin prime (107 + 109). But since there is no way to express it as the sum of the proper divisors of any other integer, it is an untouchable number. This multiplicative magic square

${\displaystyle {\begin{pmatrix}2&9&12\\36&6&1\\3&4&18\end{pmatrix}}}$

has magic constant 216.

216 is the number of digits in the decimal system of the matrix formed by the Fibonacci sequence in module $9$ for each natural number in module ${\displaystyle 9}$.^[1]

${\displaystyle 1,1,2,3,5,8,4,3,7,1,8,9,8,8,7,6,4,1,5,6,2,8,1,9}$

${\displaystyle 2,2,4,6,1,7,8,6,5,2,7,9,7,7,5,3,8,2,1,3,4,7,2,9}$

${\displaystyle 3,3,6,9,6,6,3,9,3,3,6,9,6,6,3,9,3,3,6,9,6,6,3,9}$

${\displaystyle 4,4,8,3,2,5,7,3,1,4,5,9,5,5,1,6,7,4,2,6,8,5,4,9}$

${\displaystyle 5,5,1,6,7,4,2,6,8,5,4,9,4,4,8,3,2,5,7,3,1,4,5,9}$

${\displaystyle 6,6,3,9,3,3,6,9,6,6,3,9,3,3,6,9,6,6,3,9,3,3,6,9}$

${\displaystyle 7,7,5,3,8,2,1,3,4,7,2,9,2,2,4,6,1,7,8,6,5,2,7,9}$

${\displaystyle 8,8,7,6,4,1,5,6,2,8,1,9,1,1,2,3,5,8,4,3,7,1,8,9}$

${\displaystyle 9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9}$

It has been conjectured that each natural number not equal to 216 can be written in the form ${\displaystyle p+Tx}$, where $p$ is ${\displaystyle 0}$ or a prime, and ${\displaystyle Tx=x(x+1)/2}$ is a triangular number.^[2]

In base 10, it is a Harshad number.

There are 216 fixed hexominoes, the polyominoes made from 6 squares.

216 is a Friedman number.

216 is the only number n, for which n-3,n-2,n-1,n+1,n+2,n+3 are all semiprimes.

In other fields

• The 216 colors formed by a 6×6×6 color cube are sometimes known as the web-safe color palette.
• ISO 216 is the ISO's standard for paper sizes.
• In the film Pi, Max becomes obsessed with a 216-digit number in his quest to find the numeric equation behind existence, and is told by a group of Hasidic Jews that it represents the true name of God.
• 216 is the numerical value of Gevurah, the fifth sephirot in the kabbalistic tree of life, and the sum of the letters in God's 72 hidden names.
• As six cubed (6*6*6), 216 is also symbolic of the Mark of the Beast in Christianity. This has been expressed in the Left Behind series.
• According to the Ken Burns series Baseball, it is the number of stitches on a baseball.
• +216 is the country code of Tunisia.
• (216) is the area code of Cleveland, Ohio, United States.
• The Bayon temple in Cambodia has 216 gigantic smiling faces.

See also

• The year 216

References

1. Naturalis Veritas, Massimo Nardotto, 2007 - http://216-digits.com/naturalis-veritas
2. Zhi-Wei Sun, 2009 - http://math.nju.edu.cn/~zwsun/

• Wells, D. (1987). The Penguin Dictionary of Curious and Interesting Numbers (p. 144). London: Penguin Group.