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
Senary 5006
Octal 2648
Duodecimal 13012
Hexadecimal B416

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

Contents

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 18 divisors, more 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 -sided polygon add to degrees.

In religion

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

In sports

See also

Related Research Articles

2 (two) is a number, numeral and digit. It is the natural number following 1 and preceding 3. It is the smallest and only even prime number. Because it forms the basis of a duality, it has religious and spiritual significance in many cultures.

10 (ten) is the even natural number following 9 and preceding 11. Ten is the base of the decimal numeral system, the most common system of denoting numbers in both spoken and written language.

15 (fifteen) is the natural number following 14 and preceding 16.

60 (sixty) is the natural number following 59 and preceding 61. Being three times 20, it is called threescore in older literature.

90 (ninety) is the natural number following 89 and preceding 91.

72 (seventy-two) is the natural number following 71 and preceding 73. It is half a gross or 6 dozen.

32 (thirty-two) is the natural number following 31 and preceding 33.

36 (thirty-six) is the natural number following 35 and preceding 37.

104 is the natural number following 103 and preceding 105.

<span class="mw-page-title-main">120 (number)</span> Natural number

120 is the natural number following 119 and preceding 121.

1000 or one thousand is the natural number following 999 and preceding 1001. In most English-speaking countries, it can be written with or without a comma or sometimes a period separating the thousands digit: 1,000.

300 is the natural number following 299 and preceding 301.

<span class="mw-page-title-main">360 (number)</span> Natural number

360 is the natural number following 359 and preceding 361.

127 is the natural number following 126 and preceding 128. It is also a prime number.

135 is the natural number following 134 and preceding 136.

100,000 (one hundred thousand) is the natural number following 99,999 and preceding 100,001. In scientific notation, it is written as 105.

225 is the natural number following 224 and preceding 226.

240 is the natural number following 239 and preceding 241.

252 is the natural number following 251 and preceding 253.

20,000 is the natural number that comes after 19,999 and before 20,001.

References

  1. ↑ "Positive Integers: 180".
  2. 1 2 "The Number 180". VirtueScience.com. Archived from the original on 2021-01-23. Retrieved 2009-05-29.
  3. ↑ Sloane, N. J. A. (ed.). "SequenceA002182(Highly composite numbers)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2016-05-30.
  4. ↑ "Refactorable numbers". On-Line Encyclopedia of Integer Sequences. The OEIS Foundation. 2016-04-18. Retrieved 2016-04-18.
  5. ↑ "Ulam numbers". On-Line Encyclopedia of Integer Sequences. The OEIS Foundation. 2016-04-18. Retrieved 2016-04-18.
  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
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