# 14 (number)

"Fourteen" redirects here. For other uses, see 14 (disambiguation).
"14th" redirects here. For the electronic music duo, see 14th (band).
 ← 13 14 15 →
Cardinal fourteen
Ordinal 14th
(fourteenth)
Factorization 2 × 7
Divisors 1, 2, 7, 14
Roman numeral XIV
Greek prefix tetrakaideca-
Latin prefix quattuordec-
Binary 11102
Ternary 1123
Quaternary 324
Quinary 245
Senary 226
Octal 168
Duodecimal 1212
Vigesimal E20
Base 36 E36

14 (fourteen /fɔərˈtn/) is the natural number following 13 and preceding 15.

In speech, the numbers 14 and 40 are often confused. When carefully enunciated, they differ in which syllable is stressed: 14 vs 40 /ˈfɔːrti/.[1] In relation to the word "four" (4), 14 is spelled "fourteen". In a 24-hour clock, the fourteenth hour is in conventional language called two or two o'clock.

## In mathematics

Fourteen is a composite number, its divisors being 1, 2, 7 and 14.

14 is the third discrete semiprime (2 × 7) and the 3rd member of the (2·q) discrete semiprime family. The number following 14—15—is itself a discrete semiprime and this is the first such pair of discrete semiprimes. The next example is the pair commencing 21.

The aliquot sum σ(n) of 14 is 10, also a discrete semiprime and this is again the first example of a discrete semiprime having an aliquot sum in the same form. 14 has an aliquot sequence of 6 members (14,10,8,7,1,0) 14 is the third composite number in the 7-aliquot tree.

Fourteen is itself the aliquot sum of two numbers; the discrete semiprime 22, and the square number 196.

Fourteen is the base of the tetradecimal notation.

In base fifteen and higher bases (such as hexadecimal), fourteen is represented as E.

Fourteen is the sum of the first three squares, which makes it a square pyramidal number.[2]

This number is the lowest even n for which the equation φ(x) = n has no solution, making it the first even nontotient (see Euler's totient function).[3]

14 is a Catalan number, the only semiprime among all Catalan numbers.[4]

Take a set of real numbers and apply the closure and complement operations to it in any possible sequence. At most 14 distinct sets can be generated in this way. This holds even if the reals are replaced by a more general topological space. See Kuratowski's closure-complement problem.

Fourteen is a Keith number in base 10: 1, 4, 5, 9, 14, 23, 37, 60, 97, 157...[5]

Fourteen is an open meandric number.

Fourteen is a Companion Pell number.[6]

According to the Shapiro inequality 14 is the least number n such that there exist x1, x2, …, xn such that

${\displaystyle \sum _{i=1}^{n}{\frac {x_{i}}{x_{i+1}+x_{i+2}}}<{\frac {n}{2}}}$

where xn + 1 = x1, xn + 2 = x2.

There are fourteen possible Bravais lattices that fill three-dimensional space.

The cuboctahedron, the truncated cube, and the truncated octahedron each have fourteen faces. The rhombic dodecahedron, which tessellates 3-dimensional space and is the dual of the cuboctahedron, has fourteen vertices. The truncated octahedron, which also tessellates 3-dimensional space, is the only permutohedron.

## In religion and mythology

### Islam

• The number of muqatta'at in the Quran.
• The number of Infalliables (Masoomeen) in Shia Ithna-Asheri Islam.

### Hinduism

The number of years of Rama's exile in the forests in Hinduism.

### Mythology

The number of pieces the body of Osiris was torn into by his fratricidal brother Set.

## Age 14

• Age 14 is the earliest that the emancipation of minors can occur in the U.S.
• Minimum age a person can purchase, rent or buy tickets to a 14A rated movie in Canada without an adult. Ratings are provincial, so ratings may vary. A movie can be 14A in one or some provinces and PG in other provinces. A movie can also be rated 14A in one or some provinces and 18A in other provinces. Quebec has a different rating system for films.
• Youngest age in Canada a person can watch a 14+ rated show without consent from a legal guardian.
• Minimum age at which one can view, rent, purchase, or buy tickets to an 18A rated movie with an accompanying adult in the Canadian provinces of the Maritimes and Manitoba.
• Minimum age at which one can work in many U.S states. Some require parental consent while others don't.
• Minimum age at which one can work in most Australian states with parent's consent.
• Minimum age at which one can drive a vehicle in the U.S. with a driver's license (with supervision of an adult over 18 years of age, and with a valid, unmarked driver's license, and at least 365 days of experience driving an actual automobile)
• The minimum age limit to drive a 50cc motorbike in Italy.
• The most common age of criminal responsibility in Europe.[7]

Fourteen is:

## References

1. ^ The vowels of the syllables four- and for- are identical in many dialects, such as General American and younger speakers of Received Pronunciation.
2. ^ "Sloane's A000330 : Square pyramidal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01.
3. ^ "Sloane's A005277 : Nontotients". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01.
4. ^ "Sloane's A000108 : Catalan numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01.
5. ^ "Sloane's A007629 : Repfigit (REPetitive FIbonacci-like diGIT) numbers (or Keith numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01.
6. ^ "Sloane's A002203 : Companion Pell numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01.
7. ^ Zimring, Franklin (2015). Juvenile Justice in Global Perspective. NYU Press. p. 21. ISBN 978-1-4798-9044-6. Extract of page 21
8. ^ "Johan Cruyff: Netherlands great dies of cancer aged 68". BBC Online. Retrieved 24 March 2016.
9. ^ Bowley, Roger. "14 and Shakespeare the Numbers Man". Numberphile. Brady Haran.
10. ^ Jean Ann Bowman, Jorge Luis Borges: A study of criticism in the United States, M.A. thesis submitted to and approved by the Graduate Faculty of Texas Tech University, May 1987.