131 132 133
Cardinalone hundred thirty-two
Ordinal132nd
(one hundred thirty-second)
Factorization22 × 3 × 11
Divisors1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132
Greek numeralΡΛΒ´
Roman numeralCXXXII
Binary100001002
Ternary112203
Senary3406
Octal2048
DuodecimalB012
Hexadecimal8416

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

In mathematics

132 is the sixth Catalan number.[1] It is a pronic number, the product of 11 and 12. As it has 12 divisors total, 132 is a refactorable number.

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

.

132 is the smallest number in decimal with this property,[2] which is shared by 264, 396 and 35964 (see digit-reassembly number).[3]

The number of irreducible trees with fifteen vertices is 132.[4]

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

References

  1. "Sloane's A000108 : Catalan numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-27.
  2. Wells, D. The Penguin Dictionary of Curious and Interesting Numbers London: Penguin Group. (1987): 138
  3. Sloane, N. J. A. (ed.). "Sequence A241754 (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.
  4. Sloane, N. J. A. (ed.). "Sequence A000014 (Number of series-reduced trees with n nodes.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-09-02.
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