180 (number)
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180 is a natural number that lies between 179 and 181. It is an even number and a composite number, meaning it has divisors other than 1 and itself.
In prime factorization, 180 equals 2² × 3² × 5. This composition is the reason it is divisible by many numbers, making it widely used in measurement and division.
Mathematical properties
180 has 18 divisors: 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, and 180. The sum of its divisors excluding itself exceeds 180 itself, so 180 is classified as an abundant number. It is also a Harshad number, since the sum of its digits (1+8+0 = 9) divides 180.
Because of its high number of divisors relative to smaller numbers, 180 is classified as a highly composite number. This makes it suitable for systems of division such as thirds, fifths, and sixths, all of which yield whole numbers.
Geometry and angle measurement
In the degree system, the sum of the three angles of a flat triangle equals 180 degrees. An angle of 180 degrees is called a straight angle, and it represents half of a complete circle of 360 degrees. For this reason, the phrase 'a 180' is used in some contexts to mean a complete reversal of direction.
Other uses
180 also refers to the year 180 in the Common Era and 180 BCE in history. In measurement systems and tables, such as the International Date Line at 180 degrees longitude, this number has a defining role.