180 (number)

This article is about the number. For other uses, see 180 (disambiguation).

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
Hexadecimal	B4
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]

In other fields

180 is also:

• The year AD 180 or 180 BC
• 180 is an astrological aspect considered to be negative in influence.^{[citation needed]}
• Scores on the Law School Admission Test (LSAT) are converted to a scaled score from 120 - 180.
• Lithol Rubine BK, food dye classification #E180
• John Wayne, an American film actor, starred in 180 films.
• In the Final Destination series, the number 180 is a sign of death.

See also

• List of highways numbered 180
• United Nations Security Council Resolution 180
• United States Supreme Court cases, Volume 180
• Pennsylvania House of Representatives, District 180
• United States v. Gouveia, 467 U.S. 180 (1984)

References

1. ^ "Positive Integers: 180". http://www.positiveintegers.org/180. 
2. ^ ^{a b} "The Number 180". VirtueScience.com. http://www.virtuescience.com/180.html. 
3. ^ Wells, D. (1987). The Penguin Dictionary of Curious and Interesting Numbers. London: Penguin Group. p. 142. ISBN 0-14-026149-4. 
4. ^ GNAS (2008). "Grand National Archery Society Rules of Shooting April 2008". http://www.sportfocus.com/reguser/dynabizinfo/download.cfm?number=2908. 

External links

• "180". The Number Dictionary. http://www.numdic.com/180. 
• G. L. Honaker, Jr. "Prime curiosities: 180". UTM. http://primes.utm.edu/curios/page.php/180.html.