# 180 (number)

180 (number)

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

 List of numbers — Integers << 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
Vigesimal 90

## 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]

180 is also:

## References

1. ^
2. ^ a b "The Number 180". VirtueScience.com.
3. ^ Wells, D. (1987). The Penguin Dictionary of Curious and Interesting Numbers. London: Penguin Group. p. 142. ISBN 0-14-026149-4.
4. ^

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