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216 (number)

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Title: 216 (number)  
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Subject: 217 (number), 215 (number), Plato's number, 495 (number), 420 (number)
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216 (number)

215 216 217
Cardinal two hundred sixteen
Ordinal 216th
(two hundred and sixteenth)
Factorization 23× 33
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 is a natural number.

Since 216 = 3^3 + 4^3 + 5^3 = 6^3, it is the smallest cube that's 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

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

has magic constant 216.

In base 10, it is a Harshad number.

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

216 is a Friedman number.

In other fields

See also


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