180 (number)

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← 179 180 181 →
Cardinal one hundred eighty
Ordinal 180th
(one hundred eightieth)
Factorization 22× 32× 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 101101002
Ternary 202003
Quaternary 23104
Quinary 12105
Senary 5006
Octal 2648
Duodecimal 13012
Hexadecimal B416
Vigesimal 9020
Base 36 5036

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: 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.[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]

References[edit]

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

External links[edit]