18 (number)

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"Eighteen" redirects here. For other uses, see 18 (disambiguation).
 ← 17 18 19 →
Cardinal eighteen
Ordinal 18th
(eighteenth)
Numeral system octodecimal
Factorization 2 × 32
Divisors 1, 2, 3, 6, 9, 18
Roman numeral XVIII
Binary 100102
Ternary 2003
Quaternary 1024
Quinary 335
Senary 306
Octal 228
Duodecimal 1612
Vigesimal I20
Base 36 I36

18 (eighteen) is the natural number following 17 and preceding 19.

In speech, the numbers 18 and 80 are sometimes confused. When carefully enunciated, they differ in which syllable is stressed: 18 vs 80 . However, in dates such as 1864, or when contrasting numbers in the teens, such as 17, 18, 19, the stress shifts to the first syllable: 18 . In some dialects, such as General American, there is little confusion because the single t sound in 80 becomes a d-like flap [ɾ], whereas the double t sound in 18 does not.

In mathematics

Eighteen is a composite number, its proper divisors being 1, 2, 3, 6 and 9. Three of these divisors (3, 6 and 9) add up to 18, hence 18 is a semiperfect number. Eighteen is the first inverted square-prime of the form p.q2.

It is a heptagonal number, and as the sum of the first three pentagonal numbers, it is a pentagonal pyramidal number. It is also the sum of the totient function for the first seven integers. It is the sixth lucas number.

Eighteen is the second abundant number with the aliquot sum of 21 (117% in abundance) in the aliquot sequence (18, 21, 11, 1, 0) thus being the first composite number in the 11-aliquot tree. Eighteen is the aliquot sum of only one number the square 289.

In base 10 it is a Harshad number.

18, aside from 0, is the only number that equals twice the sum of its decimal digits.

In religion and literature

• The Hebrew word for "life" is חי (chai), which has a numerical value of 18. Consequently, the custom has arisen in Jewish circles to give donations and monetary gifts in multiples of 18 as an expression of blessing for long life.
• In Judaism, in the Talmud; Pirkei Avot (5:25), Rabbi Yehudah ben Teime gives the age of 18 as the appropriate age to get married ("Ben shmonah esra lechupah", at eighteen years old to the Chupah (marriage canopy)). (See Coming of age, Age of majority).
• Shemoneh Esrei (sh'MOH-nuh ES-ray)

Lit. eighteen. A prayer that is the center of any Jewish religious service. Also known as the Amidah or the Tefilah. See Jewish Liturgy. jewfaq.org

As lucky or unlucky number

• In Chinese tradition, the number 18 is normally 十八 (shí bā), but it can also be read as 幺八 (yāo bā), which sounds like 要发 (yào fā), meaning that one is going to prosper. Thus, floors numbered "18" are often very expensive in China.[2][citation needed]

Age 18

In most countries, 18 is the age of majority.
In most countries, 18 is the voting age.
In eleven states of the United States, 18 is the age of sexual consent

• It is also the age of sexual consent under USA federal law (although this law only applies in circumstances involving transportation or transaction between different states or outside the USA).[3]
• in addition Pennsylvania has a corruption of minors law that makes the de facto age of consent there 18,[4]
• this is also the case in some jurisdictions outside the USA.[5] including Canada[6][7]

In other fields

Eighteen is also: