360 (number)

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

← 359 360 361 →
List of numbers Integers ← 0 100 200 300 400 500 600 700 800 900 →
Cardinal	three hundred sixty
Ordinal	360th (three hundred sixtieth)
Factorization	23 × 32 × 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
Greek numeral	ΤΞ´
Roman numeral	CCCLX
Binary	1011010002
Ternary	1111003
Senary	14006
Octal	5508
Duodecimal	26012
Hexadecimal	16816

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

In mathematics

360 is a highly composite number and one of only seven numbers such that no number less than twice as much has more divisors; the others are 1, 2, 6, 12, 60, and 2520 (sequence A072938 in the OEIS).

• 360 is also a superior highly composite number, a colossally abundant number, a refactorable number, a 5-smooth number, and a Harshad number in decimal since the sum of its digits (9) is a divisor of 360.

• 360 is divisible by the number of its divisors (24), and it is the smallest number divisible by every natural number from 1 to 10, except for 7. Furthermore, one of the divisors of 360 is 72, which is the number of primes below it.

• 360 is the sum of twin primes (179 + 181) and the sum of four consecutive powers of 3 (9 + 27 + 81 + 243).

• 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 angular measurement. 360° = 2π rad is also called a round angle. This unit choice divides round angles into equal sectors measured in integer rather than fractional degrees. Many angles commonly appearing in planimetrics have an integer number of degrees. For a simple non-intersecting polygon, the sum of the internal angles of a quadrilateral always equals 360 degrees.

References

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

External links

• Media related to 360 (number) at Wikimedia Commons