56 (fifty-six) is the natural number following 55 and preceding 57.
Mathematics
thumb|right|Regular 56-gon, associated by the Pythagoreans with [[Typhon]]
56 is a composite number with prime factorization <math>2^3\cdot7</math>. 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 <math>56=28+14+8+4+2</math>.
56 is a tetrahedral number, since <math>56=\binom{8}{3}</math>. It is also a pronic number, since <math>56=7\cdot8</math>, 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 <math>E_7</math> 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" (, in Portuguese), making it a widely repeated jargon in Brazil.