# 204 (number)

__: Natural number__

**Short description**
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Cardinal | two hundred four | |||

Ordinal | 204th (two hundred fourth) | |||

Factorization | 2^{2} × 3 × 17 | |||

Divisors | 1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102, 204 | |||

Greek numeral | ΣΔ´ | |||

Roman numeral | CCIV | |||

Binary | 11001100_{2} | |||

Ternary | 21120_{3} | |||

Quaternary | 3030_{4} | |||

Quinary | 1304_{5} | |||

Senary | 540_{6} | |||

Octal | 314_{8} | |||

Duodecimal | 150_{12} | |||

Hexadecimal | CC_{16} | |||

Vigesimal | A4_{20} | |||

Base 36 | 5O_{36} |

**204** (**two hundred [and] four**) is the natural number following 203 and preceding 205.

## In mathematics

204 is a refactorable number.^{[1]} 204 is a square pyramidal number: 204 balls may be stacked in a pyramid whose base is an 8 × 8 square.^{[2]} Its square, 204^{2} = 41616, is the fourth square triangular number.^{[3]} As a figurate number, 204 is also a nonagonal number^{[4]} and a truncated triangular pyramid number.^{[5]} 204 is a member of the Mian-Chowla sequence.^{[6]}

There are exactly 204 irreducible quintic polynomials over a four-element field,^{[7]} exactly 204 ways to place three non-attacking chess queens on a 5 × 5 board,^{[8]} exactly 204 squares of an infinite chess move that are eight knight's moves from the center,^{[9]} exactly 204 strings of length 11 over a three-letter alphabet with no consecutively-repeated substring,^{[10]} and exactly 204 ways of immersing an oriented circle into the oriented plane so that it has four double points.^{[11]}

Both 204 and its square are sums of a pair of twin primes: 204 = 101 + 103 and 204^{2} = 41616 = 20807 + 20809. The only smaller numbers with the same property are 12 and 84.^{[12]}

204 is a sum of all the perfect squares from 1 to 64 (i.e. 1^{2} + 2^{2} + 3^{2} + 4^{2} + 5^{2} + 6^{2} + 7^{2} + 8^{2} = 204).

## In other fields

- In telecommunications, area code 204 is a North American telephone area code for the Canadian province of Manitoba. 204 is one of the original 86 area codes assigned in 1947 in the contiguous United States and the then-nine-province extent of Canada. More recently a second area code (431) was added to allow for the expanding phone number distribution within the province.
- 204 is the HTTP status code indicating the request was successfully fulfilled and that there is no additional content to send in the response payload body.
^{[13]} - In a poker deck with a single wild joker, there are 204 hands that are at least as good as a straight flush.
^{[14]} - Model 204 is a database management system.

## References

- ↑ Sloane, N. J. A., ed. "Sequence A033950 (Refactorable numbers)". OEIS Foundation. https://oeis.org/A033950. Retrieved 2016-04-18.
- ↑ Sloane, N. J. A., ed. "Sequence A000330 (Square pyramidal numbers)". OEIS Foundation. https://oeis.org/A000330.
- ↑ Sloane, N. J. A., ed. "Sequence A001109 (a(n)^2 is a triangular number)". OEIS Foundation. https://oeis.org/A001109.
- ↑ Sloane, N. J. A., ed. "Sequence A001106 (9-gonal (or enneagonal or nonagonal) numbers)". OEIS Foundation. https://oeis.org/A001106.
- ↑ Sloane, N. J. A., ed. "Sequence A051937 (Truncated triangular pyramid numbers)". OEIS Foundation. https://oeis.org/A051937.
- ↑ Sloane, N. J. A., ed. "Sequence A005282 (Mian-Chowla Sequence)". OEIS Foundation. https://oeis.org/A005282. Retrieved 2016-04-19.
- ↑ Sloane, N. J. A., ed. "Sequence A027377 (Number of irreducible polynomials of degree n over GF(4); dimensions of free Lie algebras)". OEIS Foundation. https://oeis.org/A027377.
- ↑ Sloane, N. J. A., ed. "Sequence A047659 (Number of ways to place 3 nonattacking queens on an n X n board)". OEIS Foundation. https://oeis.org/A047659.
- ↑ Sloane, N. J. A., ed. "Sequence A018842 (Number of squares on infinite chess-board at n knight's moves from center)". OEIS Foundation. https://oeis.org/A018842.
- ↑ Sloane, N. J. A., ed. "Sequence A006156 (Number of ternary squarefree words of length n)". OEIS Foundation. https://oeis.org/A006156.
- ↑ Sloane, N. J. A., ed. "Sequence A008980 (Number of immersions of the oriented circle into the oriented plane with n double points)". OEIS Foundation. https://oeis.org/A008980..
- ↑ Sloane, N. J. A., ed. "Sequence A213784 (Numbers n such both n and n^2 are sums of a twin prime pair)". OEIS Foundation. https://oeis.org/A213784.
- ↑ Hypertext Transfer Protocol (HTTP/1.1): Semantics and Content, itef.org, retrieved 2014-07-29.
- ↑ Sloane, N. J. A., ed. "Sequence A057804 (Number of ways of getting at least ... in wild-card poker with 1 joker)". OEIS Foundation. https://oeis.org/A057804. See also OEIS: A057807.

Original source: https://en.wikipedia.org/wiki/204 (number).
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