# 116 (number)

| ||||
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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} | |||

Quaternary |
1310_{4} | |||

Quinary |
431_{5} | |||

Senary |
312_{6} | |||

Octal |
164_{8} | |||

Duodecimal |
98_{12} | |||

Hexadecimal |
74_{16} | |||

Vigesimal |
5G_{20} | |||

Base 36 |
38_{36} |

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

## In mathematics[edit]

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 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]}

## In other fields[edit]

**One hundred sixteen** is also:

- The prefix for several EU-wide telephone helplines designated as harmonised service of social value
- The atomic number of livermorium
- The number of years that the Hundred Years' War between France and England, from 1337 to 1453, actually lasted
- The fire emergency telephone number in Peru
- The record for number of wins in a single season of Major League Baseball achieved by the Chicago Cubs in 1906 and the Seattle Mariners in 2001.
- The number of pages in the Lost 116 pages, the original manuscript of what Joseph Smith said was the translation of the Book of Lehi, of the Golden plates revealed to him in 1827

## See also[edit]

- List of highways numbered 116
- 116th Street (Manhattan)
- 116th Street Crew, a mafia crew named after the Manhattan street
- The 116 Clique, a group of Christian rappers from Dallas, TX named after the Bible verse Romans 1:16

## References[edit]

**^**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..