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

In mathematics [ edit ]

• 360 is a highly composite number ^[1] 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 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 three (9 + 27 + 81 + 243 ).

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

• 360 is a triangular matchstick number. ^[2]

• 360 is the product of the first two unitary perfect numbers : ^[3] ${\displaystyle 60\times 6=360.}$

• There are 360 even permutations of 6 elements. They form the alternating group A ₆ .

A circle is divided into 360 degrees for angular measurement . 360° = 2 π   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.

Integers from 361 to 369 [ edit ]

361 [ edit ]

${\displaystyle 361=19^{2},}$ centered triangular number, ^[4] centered octagonal number , centered decagonal number , ^[5] member of the Mian?Chowla sequence , ^[6] . There are also 361 positions on a standard 19 × 19 Go board.

362 [ edit ]

${\displaystyle 362=2\times 181=\sigma _{2}(19)}$: sum of squares of divisors of 19, ^[7] Mertens function returns 0, ^[8] nontotient, noncototient. ^[9]

363 [ edit ]

364 [ edit ]

${\displaystyle 364=2^{2}\times 7\times 13}$, tetrahedral number , ^[10] sum of twelve consecutive primes (11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53), Mertens function returns 0, ^[11] nontotient .

It is a repdigit in bases three (111111), nine (444), twenty-five (EE), twenty-seven (DD), fifty-one (77), and ninety (44); the sum of six consecutive powers of three (1 + 3 + 9 + 27 + 81 + 243); and the twelfth non-zero tetrahedral number . ^[12]

365 [ edit ]

366 [ edit ]

${\displaystyle 366=2\times 3\times 61,}$ sphenic number , ^[13] Mertens function returns 0, ^[14] noncototient, ^[15] number of complete partitions of 20, ^[16] 26-gonal and 123-gonal. There are also 366 days in a leap year .

367 [ edit ]

367 is a prime number, Perrin number , ^[17] happy number , prime index prime and a strictly non-palindromic number.

368 [ edit ]

${\displaystyle 368=2^{4}\times 23.}$ It is also a Leyland number . ^[18]

369 [ edit ]

References [ edit ]

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Sources [ edit ]

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

External links [ edit ]

• Media related to 360 (number) at Wikimedia Commons