180 (number)

From HandWiki
Short description: Natural number
← 179 180 181 →
Cardinalone hundred eighty
Ordinal180th
(one hundred eightieth)
Factorization22 × 32 × 5
Divisors1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180
Greek numeralΡΠ´
Roman numeralCLXXX
Binary101101002
Ternary202003
Quaternary23104
Quinary12105
Senary5006
Octal2648
Duodecimal13012
HexadecimalB416
Vigesimal9020
Base 365036

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

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.[3] 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 Harshad number and a refactorable number.[4]

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.[5]

180 is a 61-gonal number,[2] while 61 is the 18th prime number.

Half a circle has 180 degrees,[6] and thus a U-turn is also referred to as a 180.

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

In binary it is a digitally balanced number, since its binary representation has the same number of zeros as ones (10110100).

A triangle has three interior angles that collectively total 180 degrees. In general, the interior angles of an [math]\displaystyle{ n }[/math]-sided polygon add to [math]\displaystyle{ (n-2) \times 180 }[/math] degrees.

In religion

The Book of Genesis says that Isaac died at the age of 180.[7]

In sports

  • 180 is the highest score possible with three darts.

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

References

  1. "Positive Integers: 180". http://www.positiveintegers.org/180. 
  2. 2.0 2.1 "The Number 180". VirtueScience.com. http://www.virtuescience.com/180.html. 
  3. Sloane, N. J. A., ed. "Sequence A002182 (Highly composite numbers)". OEIS Foundation. https://oeis.org/A002182. Retrieved 2016-05-30. 
  4. "Refactorable numbers". The OEIS Foundation. 2016-04-18. https://oeis.org/A033950. 
  5. "Ulam numbers". The OEIS Foundation. 2016-04-18. https://oeis.org/A002858. 
  6. Wells, D. (1987). The Penguin Dictionary of Curious and Interesting Numbers. London: Penguin Group. p. 142. ISBN 0-14-026149-4. 
  7. Genesis 35:28-29

External links