56 (number)

← 55 56 57 →
← 50 51 52 53 54 55 56 57 58 59 → List of numbers Integers ← 0 10 20 30 40 50 60 70 80 90 →
Cardinal	fifty-six
Ordinal	56th (fifty-sixth)
Factorization	23 × 7
Divisors	1, 2, 4, 7, 8, 14, 28, 56
Greek numeral	ΝϚ´
Roman numeral	LVI, lvi
Binary	1110002
Ternary	20023
Senary	1326
Octal	708
Duodecimal	4812
Hexadecimal	3816

56 (fifty-six) is the natural number following 55 and preceding 57.

Mathematics

Regular 56-gon, associated by the Pythagoreans with Typhon

56 is a composite number with prime factorization $2^{3}\cdot 7$. Its proper divisors are 1, 2, 4, 7, 8, 14, and 28, whose sum is 64, so 56 is an abundant number. It is also a semiperfect number, since $56=28+14+8+4+2$.

56 is a tetrahedral number, since $56={\binom {8}{3}}$. It is also a pronic number, since $56=7\cdot 8$, and a tetranacci number.

56 is an Erdős–Woods number, meaning that there is an interval of 57 consecutive integers in which every element has a nontrivial common factor with one of the two endpoints.

In Lie theory, the exceptional Lie algebra $E_{7}$ has a fundamental representation of dimension 56.

Mythology

Plutarch states that the Pythagoreans associated a polygon of 56 sides with Typhon and that they associated certain polygons of smaller numbers of sides with other figures in Greek mythology.

Organizations

• The symbol of the Hungarian Revolution of 1956.
• Brazilian politician Enéas Carneiro had an odd way of repeating the number of his party, "Fifty-Six" (cinquenta e seis, in Portuguese), making it a widely repeated jargon in Brazil.