# 232 (number)

**232** (**two hundred [and] thirty-two**) is the natural number following 231 and preceding 233.

| ||||
---|---|---|---|---|

Cardinal | two hundred thirty-two | |||

Ordinal |
232nd (two hundred thirty-second) | |||

Factorization |
2^{3}× 29 | |||

Prime | no | |||

Greek numeral | ΣΛΒ´ | |||

Roman numeral | CCXXXII | |||

Binary |
11101000_{2} | |||

Ternary |
22121_{3} | |||

Quaternary |
3220_{4} | |||

Quinary |
1412_{5} | |||

Senary |
1024_{6} | |||

Octal |
350_{8} | |||

Duodecimal |
174_{12} | |||

Hexadecimal |
E8_{16} | |||

Vigesimal |
BC_{20} | |||

Base 36 |
6G_{36} |

232 is both a central polygonal number^{[1]} and a cake number.^{[2]}
It is both a decagonal number^{[3]} and a centered 11-gonal number.^{[4]} It is also
a refactorable number,^{[5]}
a Motzkin sum,^{[6]}
an idoneal number,^{[7]}
and a noncototient.^{[8]}

232 is a telephone number: in a system of seven telephone users, there are 232 different ways of pairing up some of the users.^{[9]}^{[10]}
There are also exactly 232 different eight-vertex connected indifference graphs, and 232 bracelets with eight beads of one color and seven of another.^{[11]} Because this number has the form 232 = 4^{4} − 4!, it follows that there are exactly 232 different functions from a set of four elements to a proper subset of the same set.^{[12]}

## References[edit]

**^**Sloane, N.J.A. (ed.). "Sequence A000124 (Central polygonal numbers (the Lazy Caterer's sequence))".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation.**^**Sloane, N.J.A. (ed.). "Sequence A000125 (Cake numbers)".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation.**^**Sloane, N.J.A. (ed.). "Sequence A001107 (10-gonal (or decagonal) numbers)".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation.**^**Sloane, N.J.A. (ed.). "Sequence A069125 (Centered 11-gonal numbers)".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation..**^**Sloane, N.J.A. (ed.). "Sequence A033950 (Refactorable numbers: number of divisors of n divides n)".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation.**^**Sloane, N.J.A. (ed.). "Sequence A005043 (Motzkin sums)".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation.**^**Sloane, N.J.A. (ed.). "Sequence A000926 (Euler's "numerus idoneus" (or "numeri idonei", or idoneal, or suitable, or convenient numbers))".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation.**^**Sloane, N.J.A. (ed.). "Sequence A005278 (Noncototients)".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation.**^**Sloane, N.J.A. (ed.). "Sequence A000085 (Number of self-inverse permutations on n letters, also known as involutions)".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation.**^**Peart, Paul; Woan, Wen-Jin (2000), "Generating functions via Hankel and Stieltjes matrices" (PDF),*Journal of Integer Sequences*,**3**(2), Article 00.2.1, MR 1778992.**^**Sloane, N.J.A. (ed.). "Sequence A007123 (Number of connected unit interval graphs with n nodes)".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation.**^**Sloane, N.J.A. (ed.). "Sequence A036679 (n^n - n!)".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation.

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