114 (number)

Short description: Natural number

← 113 114 115 →
← 110 111 112 113 114 115 116 117 118 119 → List of numbers — Integers ← 0 100 200 300 400 500 600 700 800 900 →
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	11100102
Ternary	110203
Quaternary	13024
Quinary	4245
Senary	3106
Octal	1628
Duodecimal	9612
Hexadecimal	7216
Vigesimal	5E20
Base 36	3636

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

In mathematics

• 114 is an abundant number, a sphenic number and a Harshad number. 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 a³ + b³ + c³, 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.)
• There is no answer to the equation φ(x) = 114, making 114 a nontotient.
• 114 appears in the Padovan sequence, 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)