360 (number)

This article is about the number. For the year in the 4th century, see 360. For other uses, see 360 (disambiguation).

← 359 361 → 360
List of numbers — Integers ← 0 100 200 300 400 500 600 700 800 900 →
Cardinal	three hundred [and] sixty
Ordinal	360th (three hundred [and] sixtieth)
Factorization	$2^3 \cdot 3^2 \cdot 5$
Divisors	1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360
Roman numeral	CCCLX
Binary	1011010002
Octal	5508
Duodecimal	26012
Hexadecimal	16816
Vigesimal: $\textstyle{\mbox{I}0}$

360 (three hundred and sixty) or three sixty is the natural number following 359 and preceding 361.

In mathematics

• Divisors are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180 and 360. (A total of 24 divisors.)

• 360 makes a highly composite number. Not only is 360 highly composite, but also no number less than twice as much has more divisors(sequence A072938 in OEIS) 360 is also a superior highly composite number, a colossally abundant number and a 5-smooth number.

• 360 is the smallest number divisible by every natural number from 1 to 10 except 7.

• One of 360's divisors is 72, which is the number of primes below it.

• The sum of Euler's totient function φ(x) over the first thirty-four integers is 360.

• A circle is divided into 360 degrees for the purpose of angular measurement. 360° = 2 π rad is also called a round angle. This choice of unit allows round angle to be divided into equal sectors measured in integer degrees rather than fractional degrees. Many angles commonly appearing in planimetrics have integer number of degrees.

• 360 is the sum of two twin primes (179 + 181).

In other fields

• The term "360" (assumed 360°, see above) refers to a trick in certain sports such as Freestyle skiing, Motorcycle stunt riding, ice dancing, and acrobatics, where the athlete rotates in the air a full 360 degrees.
• A year is roughly calculated as 360 days; see 360-day calendar.
• "360" is shorthand for panoramic photographs and virtual reality worlds, since it is the degree measurement of a circle.
• 360 is a telephone area code for most of Western Washington state (includes Bellingham, Aberdeen, Olympia, but excludes Seattle area, which is area code 206).
• 360 is the U.S. Citizenship and Immigration Services I-form Petition for Amerasian, Widow(er), or Special Immigrant.
• 360 is a famous model of electric guitar built by Rickenbacker Corporation.
• Microsoft Xbox 360, a game console released in the second half of 2000s.

References

• Wells, D. (1987). The Penguin Dictionary of Curious and Interesting Numbers (p. 152). London: Penguin Group.