132 (number)

132 (one hundred [and] thirty-two) is the natural number following 131 and preceding 133. It is 11 dozens.

← 131 132 133 →
← 130 131 132 133 134 135 136 137 138 139 → List of numbers Integers ← 0 100 200 300 400 500 600 700 800 900 →
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, cxxxii
Binary	100001002
Ternary	112203
Senary	3406
Octal	2048
Duodecimal	B012
Hexadecimal	8416

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:

${\displaystyle 12+13+21+23+31+32=132}$.

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 ${\displaystyle 15\times 15}$ 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

• Refers to the Yo Soy 132 movement to vote in 2012 Mexican elections against PRI candidate Enrique Peña Nieto.