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**116** (**one hundred [and] sixteen**) is the natural number following 115 and preceding 117.

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Cardinal | one hundred sixteen | |||

Ordinal | 116th (one hundred sixteenth) | |||

Factorization | 2^{2} × 29 | |||

Divisors | 1, 2, 4, 29, 58, 116 | |||

Greek numeral | ΡΙϚ´ | |||

Roman numeral | CXVI | |||

Binary | 1110100_{2} | |||

Ternary | 11022_{3} | |||

Octal | 164_{8} | |||

Duodecimal | 98_{12} | |||

Hexadecimal | 74_{16} |

116 is a noncototient, meaning that there is no solution to the equation *m* − *φ*(*m*) = *n*, where φ stands for Euler's totient function.^{[1]}

116! + 1 is a factorial prime.^{[2]}

There are 116 ternary Lyndon words of length six, and 116 irreducible polynomials of degree six over a three-element field, which form the basis of a free Lie algebra of dimension 116.^{[3]}

There are 116 different ways of partitioning the numbers from 1 through 5 into subsets in such a way that, for every *k*, the union of the first *k* subsets is a consecutive sequence of integers.^{[4]}

There are 116 different 6×6 Costas arrays.^{[5]}

**^**Sloane, N. J. A. (ed.). "Sequence A005278 (Noncototients: n such that x-phi(x)=n has no solution)".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation..**^**Sloane, N. J. A. (ed.). "Sequence A002981 (Numbers n such that n! + 1 is prime)".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation..**^**Sloane, N. J. A. (ed.). "Sequence A027376 (Number of ternary irreducible polynomials of degree n; dimensions of free Lie algebras)".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation..**^**Sloane, N. J. A. (ed.). "Sequence A007052 (Number of order-consecutive partitions of n)".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation..**^**Sloane, N. J. A. (ed.). "Sequence A008404 (Number of Costas arrays of order n, counting rotations and flips as distinct)".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation..