360 (number) - in Mathematics

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 is one of only 7 numbers such that 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).