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# 116 (number)

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

116
Cardinal one hundred [and] sixteen
Ordinal 116th
(one hundred [and] sixteenth)
Numeral system 114
Factorization $2^2 \cdot 29$
Divisors 1, 2, 4, 29, 58, 116
Roman numeral CXVI
Binary 11101002
Octal 1648
Duodecimal 9812

## In mathematics

116 is a noncototient, meaning that there is no solution to the equation mφ(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

One hundred sixteen is also:

## References

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