# 114 (number)

From HandWiki

__: Natural number__

**Short description**
| ||||
---|---|---|---|---|

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} | |||

Quaternary | 1302_{4} | |||

Quinary | 424_{5} | |||

Senary | 310_{6} | |||

Octal | 162_{8} | |||

Duodecimal | 96_{12} | |||

Hexadecimal | 72_{16} | |||

Vigesimal | 5E_{20} | |||

Base 36 | 36_{36} |

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

## In mathematics

- 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).

## In religion

There are 114 chapters, or surahs, in the Quran.

There are 114 sayings in The Gospel of Thomas.

## See also

- 114 (disambiguation)

## References

- ↑ "Sloane's A007304 : Sphenic numbers". OEIS Foundation. https://oeis.org/A007304.
- ↑ "Sloane's A005349 : Niven (or Harshad) numbers". OEIS Foundation. https://oeis.org/A005349.
- ↑ Houston, Robin (2019-09-06). "42 is the answer to the question "what is (-80538738812075974)
^{3}+ 80435758145817515^{3}+ 12602123297335631^{3}?"" (in en). https://aperiodical.com/2019/09/42-is-the-answer-to-the-question-what-is-80538738812075974%c2%b3-80435758145817515%c2%b3-12602123297335631%c2%b3/. - ↑ "Sloane's A005277 : Nontotients". OEIS Foundation. https://oeis.org/A005277.
- ↑ "Sloane's A000931 : Padovan sequence". OEIS Foundation. https://oeis.org/A000931.

Original source: https://en.wikipedia.org/wiki/114 (number).
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