132 (number)

Last updated
131 132 133
Cardinal one hundred thirty-two
Ordinal 132nd
(one hundred thirty-second)
Factorization 22 × 3 × 11
Divisors 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132
Greek numeral ΡΛΒ´
Roman numeral CXXXII
Binary 100001002
Ternary 112203
Senary 3406
Octal 2048
Duodecimal B012
Hexadecimal 8416

132 (one hundred [and] thirty-two) is the natural number following 131 and preceding 133.

Contents

In mathematics

132 is the sixth Catalan number. [1] With twelve divisors total where 12 is one of them, 132 is the 20th refactorable number, preceding the triangular 136. [2]

132 is an oblong number, as the product of 11 and 12 [3] whose sum instead yields the 9th prime number 23; [4] on the other hand, 132 is the 99th composite number. [5]

Adding all two-digit permutation subsets of 132 yields the same number:

.

132 is the smallest number in decimal with this property, [6] which is shared by 264, 396 and 35964 (see digit-reassembly number). [7]

The number of irreducible trees with fifteen vertices is 132. [8]

In a toroidal board in the n–Queens problem, 132 is the count of non-attacking queens, [9] with respective indicator of 19 [10] and multiplicity of 1444 = 38 2 [11] (where, 2 × 19 = 38). [12]

The exceptional outer automorphism of symmetric group S6 uniquely maps vertices to factorizations and edges to partitions in the graph factors of the complete graph with six vertices (and fifteen edges) K6, which yields 132 blocks in Steiner system S(5,6,12).

In other fields

132 is also:

See also

Related Research Articles

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.

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.

92 (ninety-two) is the natural number following 91 and preceding 93.

104 is the natural number following 103 and preceding 105.

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.

400 is the natural number following 399 and preceding 401.

500 is the natural number following 499 and preceding 501.

700 is the natural number following 699 and preceding 701.

2000 is a natural number following 1999 and preceding 2001.

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.

168 is the natural number following 167 and preceding 169.

240 is the natural number following 239 and preceding 241.

232 is the natural number following 231 and preceding 233.

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".

744 is the natural number following 743 and preceding 745.

888 is the natural number following 887 and preceding 889.

References

  1. "Sloane's A000108 : Catalan numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-27.
  2. Sloane, N. J. A. (ed.). "SequenceA033950(Refactorable numbers: number of divisors of k divides k. Also known as tau numbers.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2024-03-12.
  3. Sloane, N. J. A. (ed.). "SequenceA002378(Oblong (or promic, pronic, or heteromecic) numbers: a(n) equal to n*(n+1).)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2024-03-12.
  4. Sloane, N. J. A. (ed.). "SequenceA000040(The prime numbers.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2024-03-12.
  5. Sloane, N. J. A. (ed.). "SequenceA002808(The composite numbers.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2024-03-12.
  6. Wells, D. The Penguin Dictionary of Curious and Interesting Numbers London: Penguin Group. (1987): 138
  7. Sloane, N. J. A. (ed.). "SequenceA241754(Numbers n equal to the sum of all numbers created from permutations of d digits sampled from n)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  8. Sloane, N. J. A. (ed.). "SequenceA000014(Number of series-reduced trees with n nodes.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2023-09-02.
  9. Sloane, N. J. A. (ed.). "SequenceA054502(Counting sequence for classification of nonattacking queens on n X n toroidal board.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2024-02-10.
  10. Sloane, N. J. A. (ed.). "SequenceA054500(Indicator sequence for classification of nonattacking queens on n X n toroidal board.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2024-02-10.
  11. Sloane, N. J. A. (ed.). "SequenceA054501(Multiplicity sequence for classification of nonattacking queens on n X n toroidal board.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2024-02-10.
  12. I. Rivin, I. Vardi and P. Zimmermann (1994). The n-queens problem. American Mathematical Monthly. Washington, D.C.: Mathematical Association of America. 101 (7): 629–639. doi : 10.1080/00029890.1994.11997004 JSTOR   2974691