# 15 (number)

 ← 14 15 16 →
Cardinal fifteen
Ordinal 15th
(fifteenth)
Factorization 3 × 5
Divisors 1, 3, 5, 15
Roman numeral XV
Binary 11112
Ternary 1203
Quaternary 334
Quinary 305
Senary 236
Octal 178
Duodecimal 1312
Vigesimal F20
Base 36 F36
Hebrew ט"ו (Tet Vav)

15 (fifteen) is the natural number following 14 and preceding 16. In English, it is the smallest natural number with seven letters in its spelled name.

In spoken English, the numbers 15 and 50 are often confused because they sound similar. When carefully enunciated, they differ in which syllable is stressed: 15 /fɪfˈtn/ vs 50 /ˈfɪfti/. However, in dates such as 1500 ("fifteen hundred") or when contrasting numbers in the teens, the stress generally shifts to the first syllable: 15 /ˈfɪftn/. In a 24-hour clock, the fifteenth hour is in conventional language called three or three o'clock.

## In mathematics

15 is:

There are 15 perfect matchings of the complete graph K6 and 15 rooted binary trees with four labeled leaves, both of these being among the types of object counted by double factorials. With only two exceptions, all prime quadruplets enclose a multiple of 15, with 15 itself being enclosed by the quadruplet (11, 13, 17, 19).

The 15 perfect matchings of K6

The aliquot sum of 15 is 9, a square prime 15 has an aliquot sequence of 6 members (15,9,4,3,1,0). 15 is the fourth composite number in the 3-aliquot tree. The abundant 12 is also a member of this tree. Fifteen is the aliquot sum of the consecutive 4-power 16, and the discrete semiprime 33.

15 and 16 form a Ruth-Aaron pair under the second definition in which repeated prime factors are counted as often as they occur.

There are 15 solutions to Znám's problem of length 7.

Because 15 is the product of distinct Fermat primes, 3 and 5, a regular polygon with 15 sides is constructible with compass and unmarked straightedge, and cos π/15 is expressible in terms of square roots (see here).

If a positive definite quadratic form with integer matrix represents all positive integers up to 15, then it represents all positive integers via the 15 and 290 theorems.

## In Pakistan

15 Madadgar is designated as an emergency number in Pakistan , for mobile phones, similar to the international GSM emergency number 112; if 112 is used in Pakistan, then the call is routed to 15. 112 can be used in an emergency even if the phone is locked and does not have a SIM card in it.

## In Sunnism

The Hanbali Sunni madhab states that the age of fifteen of a solar or lunar calendar is when one's taklif (obligation or responsibility) begins and is the stage whereby one has his deeds recorded.[5]

## Age 15

Age 15 is:

• The age of a quinceañera, a Hispanic girl celebrating her 15th birthday. Thus, Spanish bingo callers might refer to the number 15 as la niña bonita (the beautiful girl).
• The age for obtaining a driver's (or learner's) permit in certain jurisdictions, including some, where the legal age for a driver's license is 16.
• In the UK a minor can be sent to prison to await trial at the age of 15.
• In some countries it is the legal age for sexual intercourse.[6]
• In the UK it is the legal age to watch a BBFC "15" rated film in a cinema or purchase a "15" rated film or video game.

## In other fields

Fifteen total individuals in the mollusk species Donax variabilis comprise the entire coloration and patterning in their phenotypes.

Fifteen is:

• The number of days in each of the 24 cycles of the Chinese calendar.
• The number of guns in a gun salute to Army, Marine Corps, and Air Force Lieutenant Generals, and Navy and Coast Guard Vice Admirals.
• The number of checkers each side has at the start of a backgammon game.
• The 15 puzzle.
• The number of balls in the eight ball variant of billiards
• The number of minutes in one quarter of an hour; 15 minutes past or before an hour is often known as quarter past and quarter to, respectively.
• There are 15 Luo Points.

## References

1. "Sloane's A000384 : Hexagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01.
2. "Sloane's A000332 : Binomial coefficient binomial(n,4) = n*(n-1)*(n-2)*(n-3)/24". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01.
3. "Sloane's A000110 : Bell or exponential numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01.
4. "Sloane's A006882 : Double factorials". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01.
5. Spevack, Aaron (2011). Ghazali on the Principles of Islamic Spiritualit. p. 50.
6. Worldwide Ages of Consent. Avert.org. Retrieved on 2011-11-01.