180 (number) two square numbers: 12 + 6. It can be expressed as either the sum of six consecutive prime numbers: 19 + 23 + 29 + 31 + 37 + 41, or the sum of eight consecutive prime numbers: 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37. 180 is an Ulam number, which can be expressed as a sum of earlier terms in the Ulam sequence only as 177 + 3. 180 is a 61-gonal number. Half a circle has 180 degrees. Summing Euler's totient function φ("x") over the first + 24 integers gives
Prime number corresponds to "congruence" in modular arithmetic: formula_22 and formula_121 are congruent (written formula_122 mod formula_1) when they have the same remainder after division by formula_1. However, in this system of numbers, division by all nonzero numbers is possible if and only if the modulus is prime. For instance, with the prime number formula_125 as modulus, division by formula_28 is possible: formula_127, because clearing denominators by multiplying both sides by formula_28 gives the valid formula formula_129. However, with the composite modulus formula_130, division by formula_28 is impossible. There is no valid solution to formula_132: clearing denominators by multiplying by formula_28 causes