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**114** (**one hundred [and] fourteen**) is the natural number following 113 and preceding 115.

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Cardinal | one hundred fourteen | |||

Ordinal | 114th (one hundred fourteenth) | |||

Factorization | 2 × 3 × 19 | |||

Divisors | 1, 2, 3, 6, 19, 38, 57, 114 | |||

Greek numeral | ΡΙΔ´ | |||

Roman numeral | CXIV | |||

Binary | 1110010_{2} | |||

Ternary | 11020_{3} | |||

Octal | 162_{8} | |||

Duodecimal | 96_{12} | |||

Hexadecimal | 72_{16} |

- 114 is an abundant number, a sphenic number
^{[1]}and a Harshad number.^{[2]}It is the sum of the first four hyperfactorials, including H(0). At 114, the Mertens function sets a new low of -6, a record that stands until 197. - 114 is the smallest positive integer* which has yet to be represented as a
^{3}+ b^{3}+ c^{3}, where a, b, and c are integers. It is conjectured that 114 can be represented this way. (*Excluding integers of the form 9k ± 4, for which solutions are known not to exist.)^{[3]} - There is no answer to the equation φ(x) = 114, making 114 a nontotient.
^{[4]} - 114 appears in the Padovan sequence,
^{[5]}preceded by the terms 49, 65, 86 (it is the sum of the first two of these). - 114 is a repdigit in base 7 (222).

**^**"Sloane's A007304 : Sphenic numbers".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. Retrieved 2016-05-26.**^**"Sloane's A005349 : Niven (or Harshad) numbers".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. Retrieved 2016-05-26.**^**Houston, Robin (2019-09-06). "42 is the answer to the question "what is (-80538738812075974)^{3}+ 80435758145817515^{3}+ 12602123297335631^{3}?"".*The Aperiodical*. Retrieved 2019-12-28.**^**"Sloane's A005277 : Nontotients".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. Retrieved 2016-05-26.**^**"Sloane's A000931 : Padovan sequence".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. Retrieved 2016-05-26.