# 204 (number)

 ← 203 204 205 →
Cardinal two hundred four
Ordinal 204th
(two hundred and fourth)
Factorization 22× 3 × 17
Divisors 1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102, 204
Roman numeral CCIV
Binary 110011002
Ternary 211203
Quaternary 30304
Quinary 13045
Senary 5406
Octal 3148
Duodecimal 15012
Vigesimal A420
Base 36 5O36

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, 2042 = 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 2042 = 41616 = 20807 + 20809. The only smaller numbers with the same property are 12 and 84.[12]

## 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 the request 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]

## References

1. "Refactorable numbers". The On-Line Encyclopedia of Integer Sequences. The OEIS Foundation. 2016-04-18. Retrieved 2016-04-18.
2. "Sloane's A000330 : Square pyramidal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
3. "Sloane's A001109 : a(n)^2 is a triangular number". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
4. "Sloane's A005282 : Mian-Chowla Sequence". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-04-19. Retrieved 2016-04-19.
5. "Sloane's A047659". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
6. Hypertext Transfer Protocol (HTTP/1.1): Semantics and Content, itef.org, retrieved 2014-07-29.
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