204 (number)

Last updated
203 204 205
Cardinal two hundred four
Ordinal 204th
(two hundred fourth)
Factorization 22 × 3 × 17
Divisors 1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102, 204
Greek numeral ΣΔ´
Roman numeral CCIV
Binary 110011002
Ternary 211203
Senary 5406
Octal 3148
Duodecimal 15012
Hexadecimal CC16

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

Contents

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]

204 is a sum of all the perfect squares from 1 to 64 (i.e. 12 + 22 + 32 + 42 + 52 + 62 + 72 + 82 = 204).

In other fields

Related Research Articles

55 (fifty-five) is the natural number following 54 and preceding 56.

91 (ninety-one) is the natural number following 90 and preceding 92.

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.

360 is the natural number following 359 and preceding 361.

400 is the natural number following 399 and preceding 401.

190 is the natural number following 189 and preceding 191.

500 is the natural number following 499 and preceding 501.

700 is the natural number following 699 and preceding 701.

600 is the natural number following 599 and preceding 601.

900 is the natural number following 899 and preceding 901. It is the square of 30 and the sum of Euler's totient function for the first 54 positive integers. In base 10 it is a Harshad number. It is also the first number to be the square of a sphenic number.

2000 is a natural number following 1999 and preceding 2001.

3000 is the natural number following 2999 and preceding 3001. It is the smallest number requiring thirteen letters in English.

4000 is the natural number following 3999 and preceding 4001. It is a decagonal number.

5000 is the natural number following 4999 and preceding 5001. Five thousand is the largest isogrammic numeral in the English language.

6000 is the natural number following 5999 and preceding 6001.

225 is the natural number following 224 and preceding 226.

252 is the natural number following 251 and preceding 253.

288 is the natural number following 287 and preceding 289. Because 288 = 2 · 12 · 12, it may also be called "two gross" or "two dozen dozen".

40,000 is the natural number that comes after 39,999 and before 40,001. It is the square of 200.

References

  1. Sloane, N. J. A. (ed.). "SequenceA033950(Refactorable numbers)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2016-04-18.
  2. Sloane, N. J. A. (ed.). "SequenceA000330(Square pyramidal numbers)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  3. Sloane, N. J. A. (ed.). "SequenceA001109(a(n)^2 is a triangular number)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  4. Sloane, N. J. A. (ed.). "SequenceA001106(9-gonal (or enneagonal or nonagonal) numbers)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  5. Sloane, N. J. A. (ed.). "SequenceA051937(Truncated triangular pyramid numbers)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  6. Sloane, N. J. A. (ed.). "SequenceA005282(Mian-Chowla Sequence)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2016-04-19.
  7. Sloane, N. J. A. (ed.). "SequenceA027377(Number of irreducible polynomials of degree n over GF(4); dimensions of free Lie algebras)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  8. Sloane, N. J. A. (ed.). "SequenceA047659(Number of ways to place 3 nonattacking queens on an n X n board)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  9. Sloane, N. J. A. (ed.). "SequenceA018842(Number of squares on infinite chess-board at n knight's moves from center)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  10. Sloane, N. J. A. (ed.). "SequenceA006156(Number of ternary squarefree words of length n)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  11. Sloane, N. J. A. (ed.). "SequenceA008980(Number of immersions of the oriented circle into the oriented plane with n double points)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation..
  12. Sloane, N. J. A. (ed.). "SequenceA213784(Numbers n such both n and n^2 are sums of a twin prime pair)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  13. Hypertext Transfer Protocol (HTTP/1.1): Semantics and Content, itef.org, retrieved 2014-07-29.
  14. Sloane, N. J. A. (ed.). "SequenceA057804(Number of ways of getting at least ... in wild-card poker with 1 joker)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. See also OEIS:  A057807 .