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118 (number)

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 Title: 118 (number) Author: World Heritage Encyclopedia Language: English Subject: Collection: Integers Publisher: World Heritage Encyclopedia Publication Date:

118 (number)

 ← 117 118 119 →
Cardinal one hundred eighteen
Ordinal 118th
(one hundred and eighteenth)
Factorization 2 × 59
Divisors 1, 2, 59, 118
Roman numeral CXVIII
Binary 11101102
Ternary 111013
Quaternary 13124
Quinary 4335
Senary 3146
Octal 1668
Duodecimal 9A12
Vigesimal 5I20
Base 36 3A36

118 (one hundred [and] eighteen) is the natural number following 117 and preceding 119.

Contents

• In mathematics 1
• In telephony 2
• In other fields 3
• In dates 4
• References 6

In mathematics

There is no answer to the equation φ(x) = 118, making 118 a nontotient.

118 is the smallest n such that the range n, n + 1, ... 4n/3 contains at least one prime from each of these forms: 4x + 1, 4x - 1, 6x + 1 and 6x - 1.

Four expressions for 118 as the sum of three positive integers have the same product:

14 + 50 + 54 = 15 + 40 + 63 = 18 + 30 + 70 = 21 + 25 + 72 = 118 and
14 × 50 × 54 = 15 × 40 × 63 = 18 × 30 × 70 = 21 × 25 × 72 = 37800.

118 is the smallest number that can be expressed as four sums with the same product in this way.[1]

In other fields

One hundred and eighteen is also:

In dates

• 118 can also represent the day January 18. The 118th day of the year is April 28, on regular years. On leap years it is April 27.

References

1. ^ Wells, D. The Penguin Dictionary of Curious and Interesting Numbers London: Penguin Group. (1987): 134 - 135
2. ^ List of UK 118 directory enquiry services
3. ^ [1]
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