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Eighteen is the tenth composite number, its 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. 18 is the first inverted square-prime of the form p·q.
It is an abundant number, as the sum of its proper divisors is greater than itself (1 + 2 + 3 + 6 + 9 = 21). It is known to be a solitary number, despite not being coprime to this sum.
In base ten, it is a Harshad number, since it is divisible by the sum of its digits, 1 + 8 = 9. It is the only number in decimal where the sum of its digits is half of itself.
18 is the sum of the first even and odd primes and composites (2, 3, 4, 9), where their product is a cube, 216 = 6 (with thrice 6 being 18).
There are 18 discriminants of imaginary quadratic fields with class number 2 (negated); this is twice the number of such discriminants of class number 1 (the Heegner numbers).
18 is the number of ways to represent the word 'Floccinaucinihilipilification' using chemical element symbols.
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) is a prayer that is the center of any Jewish religious service. Its name means "eighteen". The prayer is also known as the Amidah.
Joseph Heller's novel Catch-22 was originally named Catch-18 because of the Hebrew meaning of the number, but was amended to the published title to avoid confusion with another war novel, Mila 18.
There are 18 chapters in the Bhagavad Gita, which is contained in the Mahabharata, which has 18 books. The Kurukshetra War which the epic depicts, is between 18 armies (11 on the Kuru side, 7 on the Pandava). The war itself lasts for 18 days. In the other Hindu epic, the Ramayana, the war between Rama and the demons also lasted 18 days.
In Chinese tradition, 18 is pronounced 十八; shí bā and is considered a lucky number due to similarity with 實發; shì fā 'definitely get rich', 'to get rich for sure'.
According to applications of numerology in Judaism, the letters of the word chai ("living") add up to 18. Thus, 18 is considered a lucky number and many gifts for B'nai Mitzvot and weddings are in $18 increments.
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