# 180 (number)

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Cardinal | one hundred eighty | |||

Ordinal |
180th (one hundred eightieth) | |||

Factorization |
2^{2}× 3^{2}× 5 | |||

Divisors | 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180 | |||

Greek numeral | ΡΠ´ | |||

Roman numeral | CLXXX | |||

Binary |
10110100_{2} | |||

Ternary |
20200_{3} | |||

Quaternary |
2310_{4} | |||

Quinary |
1210_{5} | |||

Senary |
500_{6} | |||

Octal |
264_{8} | |||

Duodecimal |
130_{12} | |||

Hexadecimal |
B4_{16} | |||

Vigesimal |
90_{20} | |||

Base 36 |
50_{36} |

**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 a refactorable number.^{[3]}

180 is the sum of two square numbers: 12^{2} + 6^{2}. 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.^{[4]}

180 is a 61-gonal number.^{[2]}

Half a circle has 180 degrees.^{[5]}

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 religion[edit]

The Book of Genesis says that Isaac died at the age of 180.^{[6]}

## In sports[edit]

- The maximum possible score in one turn at darts (three triple 20s).
- In archery the gent's clout shooting distance is 180 yards.
^{[7]}

## See also[edit]

- List of highways numbered 180
- United Nations Security Council Resolution 180
- United States Supreme Court cases, Volume 180
- Pennsylvania House of Representatives, District 180

## References[edit]

**^**"Positive Integers: 180".- ^
^{a}^{b}"The Number 180". VirtueScience.com. **^**"Refactorable numbers".*On-Line Encyclopedia of Integer Sequences*. The OEIS Foundation. 2016-04-18. Retrieved 2016-04-18.**^**"Ulam numbers".*On-Line Encyclopedia of Integer Sequences*. The OEIS Foundation. 2016-04-18. Retrieved 2016-04-18.**^**Wells, D. (1987).*The Penguin Dictionary of Curious and Interesting Numbers*. London: Penguin Group. p. 142. ISBN 0-14-026149-4.**^**Genesis 35:28-29**^**GNAS (2008). "Grand National Archery Society Rules of Shooting April 2008".

## External links[edit]

Wikimedia Commons has media related to .180 (number) |

- "180". The Number Dictionary.
- G. L. Honaker, Jr. "Prime curiosities: 180". UTM.