180 is an
abundant number, with its proper divisors summing up to 366. 180 is also the 11th
highly composite number, a positive integer with 18 divisors, more than any smaller positive integer. One of the consequences of 180 having so many divisors is that it is a
practical number, meaning that any positive number smaller than 180 that is not a divisor of 180 can be expressed as the sum of some of 180's divisors. 180 is a Harshad number and a
refactorable number. 180 is the
sum of two
square numbers: 122 + 62. 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, and thus a
U-turn is also referred to as a
180. Summing
Euler's totient function φ(
x) over the first +
24 integers gives 180. In
binary it is a digitally balanced number, since its binary representation has the same number of zeros as ones (10110100). A
triangle has three
interior angles that collectively total 180
degrees. In general, the interior angles of an n-sided polygon add to (n-2) \times 180 degrees. ==References==