18 (number)

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"Eighteen" and "XVIII" redirect here. For other uses, see 18 (disambiguation).
← 17 18 19 →
Cardinal eighteen
Ordinal 18th
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
Hexadecimal 1216
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 /tˈtn/ vs 80 /ˈti/. 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 /ˈttn/. 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 a 24-hour clock, the eighteenth hour is in conventional language called six or six o'clock.

In mathematics[edit]

Eighteen is a 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.[1] Eighteen is the first inverted square-prime of the form p·q2.

It is a heptagonal number,[2] and as the sum of the first three pentagonal numbers, it is a pentagonal pyramidal number.[3] It is also the sum of the totient function for the first seven integers.[4] It is the sixth lucas number.[5]

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.[6]

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

In science[edit]



In religion and literature[edit]

  • 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. See Jewish Liturgy. jewfaq.org

  • In Ancient Roman custom the number 18 can symbolise a blood relative.
  • 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.[7]
  • 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.
  • A shape looking like 18 in Arabic numbers is formed by the lines on the palm of the right hand.

As lucky or unlucky number[edit]

  • In Chinese tradition, 18 pronounced 十八 (shí bā) and is a considered lucky number due to similarity with 實發 (shì fā) 'definitely get rich', 'to get rich for sure'.[8]

Age 18[edit]

In most countries, 18 is the age of majority and also 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).[9]

In addition, Pennsylvania has a corruption of minors law that makes the de facto age of consent there 18.[10] This is also the case in some jurisdictions outside the USA,[11] including Canada[12][13]

In sports[edit]

In other fields[edit]

Eighteen is also:

See also[edit]


  1. ^ "Sloane's A005835 : Pseudoperfect (or semiperfect) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31. 
  2. ^ "Sloane's A000566 : Heptagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31. 
  3. ^ "Sloane's A002411 : Pentagonal pyramidal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31. 
  4. ^ "Sloane's A002088 : Sum of totient function". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31. 
  5. ^ "Sloane's A000032 : Lucas numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31. 
  6. ^ "Sloane's A005349 : Niven (or Harshad) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31. 
  7. ^ 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
  8. ^ 言必有「中」:「十八」「實發」 人見人愛. 文匯報. Accessed 2015-01-12. Archived 2015-01-15.
  9. ^ "The US Federal Age of Sexual Consent". SOL Research. Retrieved 2013-08-02. 
  10. ^ "Age Of Consent By State". Age-of-consent.info. Retrieved 2013-08-02. 
  11. ^ "Worldwide Ages of Consent". Avert.org. Retrieved 2013-08-02. 
  12. ^ CANADA'S LEGAL AGE OF CONSENT TO SEXUAL ACTIVITY Revised 12 April 2001: "Section 153 now prohibits "sexual interference" or "invitation to sexual touching," in respect of a young person over 14 but under 18, where the accused is in a relationship of trust or authority towards the complainant or the complainant is in a relationship of dependency with the accused."
  13. ^ Government of Canada - Age of Consent to Sexual Activity: "the age of consent is 18 years where the sexual activity "exploits" the young person -- when it involves prostitution, pornography or occurs in a relationship of authority, trust or dependency (e.g., with a teacher, coach or babysitter). Sexual activity can also be considered exploitative based on the nature and circumstances of the relationship, e.g., the young person's age, the age difference between the young person and their partner, how the relationship developed (quickly, secretly, or over the Internet) and how the partner may have controlled or influenced the young person."
  14. ^ "Eighteen One-Name Study". One-name.org. 2012-01-13. Retrieved 2013-08-02.