180 (number)

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This article is about the number. For other uses, see 180 (disambiguation).
179 180 181
Cardinal one hundred eighty
Ordinal 180th
(one hundred and eightieth)
Factorization 22× 32× 5
Divisors 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180
Roman numeral CLXXX
Binary 101101002
Ternary 202003
Quaternary 23104
Quinary 12105
Senary 5006
Octal 2648
Duodecimal 13012
Hexadecimal B416
Vigesimal 9020
Base 36 5036

180 (one hundred [and] eighty) is the natural number following 179 and preceding 181.

In mathematics[edit]

180 is an abundant number, with its proper divisors summing up to 366.[1][2] 180 is also a highly composite number, a positive integer with more divisors than any smaller positive integer. One of the consequences of 180 having so many divisors is that it is a practical number, meaning that any positive number smaller than 180 that is not a divisor of 180 can be expressed as the sum of some of 180's divisors.

180 is the sum of two square numbers: 122 + 62. It can be expressed as either the sum of six consecutive prime numbers: 19 + 23 + 29 + 31 + 37 + 41, or the sum of eight consecutive prime numbers: 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37. 180 is an Ulam number, which can be expressed as a sum of earlier terms in the Ulam sequence only as 177 + 3.

180 is a 61-gonal number.[2]

Half a circle has 180 degrees.[3]

Summing Euler's totient function φ(x) over the first + 24 integers gives 180.

180 is a Harshad number in base 10, and in binary it is a digitally balanced number, since its binary representation has the same number of zeros as ones (10110100).

In sports[edit]

  • A "180" is a trick in extreme sports where a rider rotates half a turn while airborne and lands.
  • The maximum possible score in one turn at darts (three triple 20s).
  • In archery the gent's clout shooting distance is 180 yards.[4]

In other fields[edit]

180 is also:

See also[edit]

References[edit]

External links[edit]