56 (number)

Template:Pp-pc Template:Infobox number 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 $56=(\genfrac{}{}{0ex}{}{8}{3})$. 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" (Template:Lang, in Portuguese), making it a widely repeated jargon in Brazil.