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:

• The sum of the first six triangular numbers (making it a tetrahedral number).
• The number of ways to choose 3 out of 8 objects or 5 out of 8 objects, if order does not matter.
• The sum of six consecutive primes (3 + 5 + 7 + 11 + 13 + 17)
• a tetranacci number and as a multiple of 7 and 8, a pronic number. Interestingly it is one of a few pronic numbers whose digits in decimal also are successive (5 and 6).
• a refactorable number, since 8 is one of its 8 divisors.
• The sum of the sums of the divisors of the first 8 positive integers.
• A semiperfect number, since 56 is twice a perfect number.
• A partition number – the number of distinct ways 11 can be represented as the sum of natural numbers.
• An Erdős–Woods number, since it is possible to find sequences of 56 consecutive integers such that each inner member shares a factor with either the first or the last member.
• The only known number n such that φ(n − 1)σ(n − 1) = φ(n)σ(n) = φ(n + 1)σ(n + 1), where φ(m) is Euler's totient function and σ(n) is the sum of the divisor function, see OEIS: A244439.
• The maximum determinant in an 8 by 8 matrix of zeroes and ones.
• The number of polygons formed by connecting all the 8 points on the perimeter of a two-times-two-square by straight lines.

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. While it is impossible to construct a perfect regular 56-sided polygon using a compass and straightedge, a close approximation has recently been discovered which it is claimed might have been used at Stonehenge, and it is constructible if the use of an angle trisector is allowed since 56 = 2³ × 7.

Organizations

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

Cosmogony

• According to Aristotle, 56 is the number of layers of the Universe – Earth plus 55 crystalline spheres above it.