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18
Cardinal eighteen
Ordinal 18th
(eighteenth)
Numeral system octodecimal
Factorization 2 \cdot 3^2
Divisors 1, 2, 3, 6, 9, 18
Roman numeral XVIII
Binary 100102
Octal 228
Duodecimal 1612
Hexadecimal 1216

18 (eighteen) is the natural number following 17 and preceding 19. It equals ten and eight, twice nine, nine times two or three times six.

In speech, the numbers 18 and 80 are sometimes confused. When carefully enunciated, they differ in which syllable is stressed: 18 /eɪtˈtiːn/ vs 80 /ˈeɪti/. 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 /ˈeɪttiːn/. 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.

Contents

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.

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 science

In religion and literature

As lucky or unlucky number

  • In Chinese tradition, the number 18, normally 十八 (shí bā), can also be read as 幺八 (yāo bā), which sounds like 要发 (yào fā), meaning that one is going to prosper. Thus, building floors numbered "18" are often very expensive in China[citation needed] The number 18 as in the floor 18 of a building in Northern China is viewed as a floor to be avoided as the 18 level of hell that one can never return from.

Age 18

In many countries 18 is the age of majority. See also: 18 certificate, Coming of age, Voting age

In other fields

Eighteen is also:

Historical years

See also

Notes

  1. ^ N James. The Early Composition History of Catch-22. In Biographies of Books: The Compositional Histories of Notable American Writings, J Barbour, T Quirk (edi.) pp. 262-90. Columbia: University of Missouri Press, 1996







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