180 (number)

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180 (one hundred eighty in American English, one hundred and eighty in British English) is the natural number following 179 and preceding 181.

List of numbers — Integers

<< 180 181 182 183 184 185 186 187 188 189 >>

Ordinal One hundred [and]
eighty
Cardinal 180th
Factorization [2^2 \cdot 3^2 \cdot 5]
Roman numeral CLXXX
Binary 10110100
Duodecimal 130
Hexadecimal B4
Vigesimal 90

In mathematics

One hundred [and] eighty is the sum of six consecutive primes (19 + 23 + 29 + 31 + 37 + 41), as well as the sum of eight consecutive primes (11 + 13 + 17 + 19 + 23 + 29 + 31 + 37).

The sum of Euler's totient function φ(x) over the first twenty-four integers is 180. Since 180 is divisible by the total number of its divisors, it is a refactorable number.

Using degrees (°) to measure angles, 180° is called straight angle, and makes a semicircle. 180° is equivalent to π rads. In normal space, the interior angles of a triangle add up to 180°.

180 is a Harshad number in base 10.

In other fields

180° also means antipode. For example, a "180-degree change" indicates a radical change.
Interstate 180, the designation of some spur routes of Interstate 80 in the United States.
The maximum possible score in one turn at darts (three treble 20s).
In astronomy, when two planets are 180 degrees apart, they are said to be in opposition. In astrology, this is an aspect that is considered to be negative in influence.
The year AD 180 or 180 BC.
180 is a perfect score on the LSAT. Thus, it is often used by law students and attorneys in conversation to signify agreement or appreciation of a point.
In the moves series Final Destination, Final Destination 2, and Final Destination 3, 180 is a number that often foreshadows death and suffering (FD1: Plane that blew up was Flight 180; FD2: Pile-up was on route 180; FD3: Subway car was car 180)

Other numbers in the 180s

181 = prime number, Chen prime, palindromic prime, star number, centered square number, centered pentagonal number, sum of five consecutive primes (29 + 31 + 37 + 41 + 43)

182 = 2 7 13, sphenic number, pronic number, nontotient

183 = 3 61, Middle day of the year (not leap years).

184 = 2^3 23, sum of four consecutive primes (41 + 43 + 47 + 53)

185, see 185 (number)

186 = 2 3 31, sphenic number, nontotient

187 = 11 17, sum of three consecutive primes (59 + 61 + 67), sum of nine consecutive primes (7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37), self number

188 = 2^2 47, nontotient, untouchable number

189 = 3^3 7 = 6³+(-3)³ = 4³+5³, centered cube number

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