180 (number)

180 (number)

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

List of numbersIntegers

<< 180 181 182 183 184 185 186 187 188 189 >>

Cardinal One hundred [and] eighty
Ordinal 180th
Factorization 2^2 \cdot 3^2 \cdot 5
Divisors 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180
Roman numeral CLXXX
Binary 10110100
Duodecimal 130
Hexadecimal B4
Vigesimal 90

Contents

In mathematics

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 primes: 19 + 23 + 29 + 31 + 37 + 41, or the sum of eight consecutive primes: 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

  • 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

180 is also:

See also

References

External links


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