# 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 and thirty-second) | |||

Factorization |
2^{3}× 29 | |||

Prime | no | |||

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

- ↑ "Sloane's A000124 : Central polygonal numbers (the Lazy Caterer's sequence)".
*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. - ↑ "Sloane's A000125 : Cake numbers".
*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. - ↑ "Sloane's A001107 : 10-gonal (or decagonal) numbers".
*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. - ↑ "Sloane's A069125 : Centered 11-gonal numbers".
*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation.. - ↑ "Sloane's A033950 : Refactorable numbers: number of divisors of n divides n".
*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. - ↑ "Sloane's A005043 : Motzkin sums".
*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. - ↑ "Sloane's 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's A005278 : Noncototients".
*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. - ↑ "Sloane's 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's A007123 : Number of connected unit interval graphs with n nodes".
*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. - ↑ "Sloane's A036679 : n^n - n!".
*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation.