16 (number): Difference between revisions

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Cardinal	sixteen
Ordinal	16th; (sixteenth)
Numeral system	hexadecimal
Factorization	24
Divisors	1, 2, 4, 8, 16
Greek numeral	ΙϚ´
Roman numeral	XVI, xvi
Binary	100002
Ternary	1213
Senary	246
Octal	208
Duodecimal	1412
Hexadecimal	1016
Hebrew numeral	ט"ז / י"ו
Babylonian numeral	𒌋𒐚

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16 (sixteen) is the natural number following 15 and preceding 17. It is the fourth power of two.

In English speech, the numbers 16 and 60 are sometimes confused, as they sound very similar.

Mathematics

16 is the ninth composite number, and a square number: 4² = 4 × 4 (the first non-unitary fourth-power prime of the form p⁴). It is the smallest number with exactly five divisors, its proper divisors being 1, 2, 4 and 8.

Sixteen is the only integer that equals mⁿ and n^m, for some unequal integers m and n ( $m=4$ , $n=2$ , or vice versa).^[1] It has this property because $2^{2}=2\times 2$ . It is also equal to ³2 (see tetration).

The aliquot sum of 16 is 15, within an aliquot sequence of four composite members (16, 15, 9, 4, 3, 1, 0) that belong to the prime 3-aliquot tree.

Sixteen is the largest known integer $n$ , for which $2^{n}+1$ is prime.
It is the first Erdős–Woods number.^[2]
There are 16 partially ordered sets with four unlabeled elements.^[3]

16 is the only number that can be both the perimeter and area of the same square, due to $4^{2}$ being equal to $4\times 4.$

The sedenions form a 16-dimensional hypercomplex number system.

Hexadecimal

Sixteen is the base of the hexadecimal number system, which is used extensively in computer science.

Technology

In some computer programming languages, the size in bits of certain data types
16-bit computing
A 16-bit integer can represent up to 65,536 values.
In the 16-bit era, 16-bit microprocessor ran 16-bit applications

Culture

As a unit of measurement

A low power of two, 16 was used in weighing light objects in several cultures. Early civilizations utilized the weighing scale as a means to measure mass, which made splitting resources into equal parts a simple task.^[4]^[5] In the imperial system, 16 ounces equivalates to one pound. Until the State Council of the People's Republic of China decreed a decimal conversion for currency in 1959,^[6] China equivalated 16 liǎng to one jīn. Chinese Taoists did finger computation on the trigrams and hexagrams by counting the finger tips and joints of the fingers with the tip of the thumb. Each hand can count up to 16 in such manner. The Chinese abacus uses two upper beads to represent the 5s and 5 lower beads to represent the 1s, the 7 beads can represent a hexadecimal digit from 0 to 15 in each column.

Age 16

A "sweet sixteen" is celebrated by many sixteen-year-old girls in the United States and Canada. It is a coming-of-age celebration that traditionally marks a girl's transition into womanhood.
In the United States and Canada, 16 is the most common age of sexual consent, as well as the age in the United Kingdom and several European countries.^[7]^[8] Sixteen is also the minimum age for being allowed a beginner's driver's license with parental consent in many US states and in Canada.

References

^ David Wells (1987). The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books. p. 93.
^ "Sloane's A059756 : Erdős–Woods numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 4 December 2020.
^ Sloane, N. J. A. (ed.). "Sequence A000112 (Number of partially ordered sets (posets) with n unlabeled elements)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^ Morley, Iain; Renfrew, Colin (2010). The Archaeology of Measurement: Comprehending Heaven, Earth and Time in Ancient Societies. Cambridge University Press. pp. 88–105. ISBN 9780511760822.
^ Petruso, Karl M. (1981). "Early Weights and Weighing in Egypt and the Indus Valley". M Bulletin (Museum of Fine Arts, Boston). 79: 44–51. ISSN 0739-5736. JSTOR 4171634.
^ "(in Chinese) 1959 Gazette of the State Council of the People's Republic of China". www.gov.cn. Retrieved 1 November 2024.
^ "Age of Consent By State". Archived from the original on 17 April 2011.
^ "Age of consent for sexual intercourse". Avert. Archived from the original on 22 April 2011.

External links

Symonds, Ria; Parker, Matt. "16 x^y = y^x Sweet Sixteen". Numberphile. Brady Haran. Archived from the original on 31 May 2013. Retrieved 1 April 2013.

[1] David Wells (1987). The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books. p. 93.

[2] "Sloane's A059756 : Erdős–Woods numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 4 December 2020.

[3] Sloane, N. J. A. (ed.). "Sequence A000112 (Number of partially ordered sets (posets) with n unlabeled elements)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.

[4] Morley, Iain; Renfrew, Colin (2010). The Archaeology of Measurement: Comprehending Heaven, Earth and Time in Ancient Societies. Cambridge University Press. pp. 88–105. ISBN 9780511760822.

[5] Petruso, Karl M. (1981). "Early Weights and Weighing in Egypt and the Indus Valley". M Bulletin (Museum of Fine Arts, Boston). 79: 44–51. ISSN 0739-5736. JSTOR 4171634.

[6] "(in Chinese) 1959 Gazette of the State Council of the People's Republic of China". www.gov.cn. Retrieved 1 November 2024.

[7] "Age of Consent By State". Archived from the original on 17 April 2011.

[8] "Age of consent for sexual intercourse". Avert. Archived from the original on 22 April 2011.

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@@ Line 8: / Line 8: @@
 | lang1 symbol = <span style="font-size:150%;">ט"ז / י"ו</span>
 |lang2=[[Babylonian cuneiform numerals|Babylonian numeral]]|lang2 symbol=𒌋𒐚}}
-'''16''' ('''sixteen''') is the [[natural number]] following [[15 (number)|15]] and preceding [[17 (number)|17]].
+'''16''' ('''sixteen''') is the [[natural number]] following [[15 (number)|15]] and preceding [[17 (number)|17]]. It is the [[4|fourth]] [[power of two]].
-is the ninth [[composite number]], and a [[square number]], being [[4 (number)|4]]<sup>2</sup> = 4 × 4. It is the smallest number with exactly five [[divisor]]s, its proper divisors being {{num|1}}, {{num|2}}, {{num|4}} and {{num|8}}.
-is the first non-unitary fourth-power [[prime number|prime]] of the form ''p''<sup>4</sup>
-The [[aliquot sum]] of a 2-power (2<sup>n</sup>)  is always one less than the 2-power itself therefore the aliquot sum of 16 is [[15 (number)|15]],  within an [[aliquot sequence]] of four composite members (16,[[15 (number)|15]],[[9 (number)|9]],[[4 (number)|4]],[[3 (number)|3]],[[1 (number)|1]],0) to the Prime in the 3-aliquot tree.
 In English speech, the numbers 16 and [[60 (number)|60]] are sometimes confused, as they sound very similar.
+== Mathematics ==
-Sixteen is the fourth [[power of two]]. For this reason, 16 was used in weighing light objects in several cultures. The British have 16 ounces in one pound; the Chinese used to have 16 ''liangs'' in one ''jin''. In old days{{vague|date=December 2020}}, weighing was done with a beam balance to make equal splits. It would be easier to split a heap of grains into sixteen equal parts through successive divisions than to split into ten parts. Chinese Taoists did finger computation on the trigrams and hexagrams by counting the finger tips and joints of the fingers with the tip of the thumb. Each hand can count up to 16 in such manner. The Chinese abacus uses two upper beads to represent the 5s and 5 lower beads to represent the 1s, the 7 beads can represent a hexadecimal digit from 0 to 15 in each column.
+is the ninth [[composite number]], and a [[square number]]: [[4 (number)|4]]<sup>2</sup> = 4 × 4 (the first non-unitary fourth-power [[prime number|prime]] of the form ''p''<sup>4</sup>). It is the smallest number with exactly five [[divisor]]s, its proper divisors being {{num|1}}, {{num|2}}, {{num|4}} and {{num|8}}.
+Sixteen is the only integer that [[Equation x^y = y^x|equals ''m''<sup>''n''</sup> and ''n''<sup>''m''</sup>, for some unequal integers ''m'' and ''n'']] (<math>m=4</math>, <math>n=2</math>, or vice versa).<ref>{{cite book
-== Mathematics ==
-*Sixteen is an [[Parity (mathematics)|even]] number and the square of four.
-*Sixteen is the fourth power of two.
-*Sixteen is the only integer that [[Equation x^y = y^x|equals ''m''<sup>''n''</sup> and ''n''<sup>''m''</sup>, for some unequal integers ''m'' and ''n'']] (<math>m=4</math>, <math>n=2</math>, or vice versa).<ref>{{cite book
  |author = David Wells
  |title = The Penguin Dictionary of Curious and Interesting Numbers
@@ Line 30: / Line 22: @@
  |page = 93
 }}</ref> It has this property because <math>2^{2}=2\times 2</math>. It is also equal to <sup>3</sup>2 (see [[tetration]]).
-*Sixteen is the base of the [[hexadecimal]] number system, which is used extensively in [[computer science]].
+The aliquot sum of 16 is [[15 (number)|15]], within an [[aliquot sequence]] of four composite members (16, [[15 (number)|15]], [[9 (number)|9]], [[4 (number)|4]], [[3 (number)|3]], [[1 (number)|1]], [[0]]) that belong to the prime '''3'''-aliquot tree.
 *Sixteen is the largest known integer {{mvar|n}}, for which <math>2^n+1</math> is prime.
 *It is the first [[Erdős–Woods number]].<ref>{{Cite web|url=https://oeis.org/A059756|title=Sloane's A059756 : Erdős–Woods numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2020-12-04}}</ref>
 *There are 16 partially ordered sets with four unlabeled elements.<ref>{{cite OEIS|A000112|Number of partially ordered sets (posets) with n unlabeled elements}}</ref>
-*16 is the only number that can be both the perimeter and area of the same square, due to <math>4^{2}</math> being equal to <math>4\times 4</math>
+is the only number that can be both the perimeter and area of the same square, due to <math>4^{2}</math> being equal to <math>4\times 4.</math>
-==Science==
-* The [[atomic number]] of [[sulfur]]
-* [[Group (periodic table)|Group 16]] of the [[periodic table]] are the [[chalcogens]]
+The [[sedenion]]s form a 16-dimensional [[hypercomplex number]] system.
-==In technology==
+=== Hexadecimal ===
+Sixteen is the base of the [[hexadecimal]] number system, which is used extensively in [[computer science]].
+== Technology ==
 * In some [[Programming language|computer programming languages]], the size in bits of certain data types
 * [[16-bit computing]]
 * A 16-bit integer can represent up to [[65,536#In computing|65,536]] values.
+* In the [[16-bit era]], [[16-bit]] microprocessor ran [[16-bit application]]s
-==Religion==
+== Culture ==
-=== Hinduism ===
+=== As a unit of measurement ===
+A low [[power of two]], 16 was used in weighing light objects in several cultures. Early civilizations utilized the [[weighing scale]] as a means to measure mass, which made splitting resources into equal parts a simple task.<ref>{{Cite book |last1=Morley |first1=Iain |title=The Archaeology of Measurement: Comprehending Heaven, Earth and Time in Ancient Societies |last2=Renfrew |first2=Colin |publisher=Cambridge University Press |year=2010 |isbn=9780511760822 |pages=88–105}}</ref><ref>{{Cite journal |last=Petruso |first=Karl M. |date=1981 |title=Early Weights and Weighing in Egypt and the Indus Valley |url=https://www.jstor.org/stable/4171634 |journal=M Bulletin (Museum of Fine Arts, Boston) |volume=79 |pages=44–51 |jstor=4171634 |issn=0739-5736}}</ref> In the [[Imperial units|imperial system]], 16 [[Ounce|ounces]] equivalates to one [[Pound (mass)|pound]]. Until the [[State Council of the People's Republic of China]] decreed a decimal conversion for currency in 1959,<ref>{{Cite web |title=(in Chinese) 1959 Gazette of the State Council of the People's Republic of China |url=https://www.gov.cn/zwgk/2011-11/09/content_1988933.htm |access-date=2024-11-01 |website=www.gov.cn}}</ref> China equivalated 16 ''[[Tael|liǎng]]'' to one ''[[Jin (mass)|jīn]]''. Chinese Taoists did finger computation on the trigrams and hexagrams by counting the finger tips and joints of the fingers with the tip of the thumb. Each hand can count up to 16 in such manner. The Chinese abacus uses two upper beads to represent the 5s and 5 lower beads to represent the 1s, the 7 beads can represent a hexadecimal digit from 0 to 15 in each column.
-* Saint [[Markandeya]] is said to have been granted to live to 16 years of age. When he turned sixteen, the god of death, [[Yama]], came to look for him and fastened a noose around the saint. The saint hugged the idol of lord [[Shiva]] that he worshipped (which can be still found in the [[Amritaghateswarar-Abirami Temple, Thirukkadaiyur|Amritaghateswarar-Abirami Temple]] in [[Thirukkadaiyur]], Tamil Nadu, [[India]]). As the noose was wrapped around both the saint and lord Shiva, this made the lord angry and he appeared in his fierce form and vanquished the lord of death, causing a brief catastrophe in the world where no one died. Eventually, lord Yama was revived and the saint [[Markandeya]] was made immortal to be of age sixteen forever.
-==Age 16==
+=== Age 16 ===
+* A "[[sweet sixteen (birthday)|sweet sixteen]]" is celebrated by many sixteen-year-old girls in the [[United States]] and [[Canada]]. It is a [[coming of age|coming-of-age]] celebration that [[Tradition|traditionally]] marks a girl's transition into womanhood.
-{{globalize|dat16
+* In the United States and Canada, 16 is the most common [[age of consent|age of sexual consent]], as well as the age in the United Kingdom and [[Ages of consent in Europe|several European countries]].<ref>{{cite web|url=http://www.age-of-consent.info/|archive-url=https://web.archive.org/web/20110417024317/http://www.age-of-consent.info/|url-status=dead|archive-date=2011-04-17|title=Age of Consent By State}}</ref><ref>{{cite web|url=http://www.avert.org/age-of-consent.htm|title=Age of consent for sexual intercourse|website=Avert|archive-url=https://web.archive.org/web/20110422181758/http://www.avert.org/age-of-consent.htm|url-status=dead|archive-date=2011-04-22}}</ref> Sixteen is also the minimum age for being allowed a beginner's [[driver's license]] with parental consent in many [[United States|US]] states and in [[Canada]].
-e=October 2014|date=September 2016}}
-* Sixteen is the minimum age for being allowed a beginner's [[driver's license]] with parental consent in many [[United States|US]] states and in [[Canada]]. In [[Australia]], [[Iceland]], [[New Zealand]], [[Norway]], [[South Africa]], and the [[Isle of Man]], it is the age that one is eligible to get a learner's [[license]].
-* A "[[sweet sixteen (birthday)|sweet sixteen]]" is celebrated by many sixteen-year-old girls in the [[United States]] and [[Canada]]. It is a [[coming of age|coming-of-age]] celebration that traditionally marks a girl's transition into womanhood.
-* 16 is the minimum age that one can leave school in many states of the United States and Canada (however, restrictions apply and vary depending on state or province).<ref name="ECS">{{cite web|first=Marga|last=Mikulecky|publisher=Education Commission of the States|title=Compulsory School Age Requirements|url=http://www.ecs.org/clearinghouse/01/07/03/10703.pdf|date=April 2013|access-date=8 January 2015}}</ref>
-* In the United States, sixteen-year-old girls earn the right to privacy laws surrounding [[Obstetrics and gynaecology|OBGYN]] practices
-* In the United States and Canada, 16 is the most common [[age of consent|age of sexual consent]], as well as the age in the United Kingdom and [[Ages of consent in Europe|several European countries]].<ref>{{cite web|url=http://www.age-of-consent.info/|archive-url=https://web.archive.org/web/20110417024317/http://www.age-of-consent.info/|url-status=dead|archive-date=2011-04-17|title=Age of Consent By State}}</ref><ref>{{cite web|url=http://www.avert.org/age-of-consent.htm|title=Age of consent for sexual intercourse|website=Avert|archive-url=https://web.archive.org/web/20110422181758/http://www.avert.org/age-of-consent.htm|url-status=dead|archive-date=2011-04-22}}</ref>
-* Sixteen is the minimum age to get married with parental consent in many countries, and without parental consent in [[Scotland]].
-* Sixteen is the [[legal drinking age]] in [[Germany]], [[Belgium]], [[Switzerland]], [[Austria]] and [[Portugal]].
-* Minimum age at which one can buy, rent, purchase, buy tickets to, or view a 16+ rated film in the Canadian province of Quebec. It is also the minimum age at which one can accompany a minor under 13 while buying, renting, or purchasing tickets to a 13+ rated movie in the province of Quebec.
-* Minimum age at which one can donate blood (with parental consent) in many US states.
-* Minimum age at which one can obtain an adult passport (which lasts ten years) in the United States, United Kingdom, and Australia.
-* Minimum age at which one can join the [[British Armed Forces]].
-* Sixteen is the voting age in [[Argentina]], [[Austria]], [[Brazil]], [[Cuba]], [[Ecuador]], the [[Isle of Man]], and [[Nicaragua]].
-* Sixteen is the [[age of majority]] in [[Cambodia]], [[Cuba]], [[Kyrgyzstan]], and [[Vietnam]].
-==In sports==
-Many leagues and tournaments have 16 teams or individual participants, for example:
-* [[FIFA World Cup]] finals from 1934 through 1978 (although for various reasons, only 15 competed in the 1938 and 1950 finals)
-* [[FIFA World Cup]] knockout phase since 1986.
-* [[FIFA Women's World Cup]] finals from 1999 through 2011
-* The season-ending [[NASCAR playoffs|playoffs]] in the [[Monster Energy NASCAR Cup Series|NASCAR Cup Series]]
-* The [[National League (baseball)|National League]] of [[Major League Baseball]] from 1998 to 2012
-In both the [[NBA]] and [[NHL]], 16 teams qualify for the respective league playoffs; it is also the number of wins needed to win the title (both leagues have four playoff rounds, with four wins in seven games needed to win each round).
-From 1978 to 2020, the NFL operated with 16 games in the regular season.
-In [[AFL Women's]], the top-level league of [[women's Australian rules football]], each team has 16 players on the field at any given time (as opposed to the 18 of almost all other competitions in the sport, most notably the parent [[Australian Football League]] for men).
-==In other fields==
-{{See also|List of highways numbered 16}}
-* 16 steps make up the average bar of music in a 4/4 musical arrangement. The [[Roland TR-808]], for instance, has 16 buttons that light up representing 16 16th notes making up a drum pattern.
-*[[Sixteen, Kentucky]], a community in the United States
-* King of France (August 1754 – 21 January 1793) [[Louis XVI of France]]
-* There are 16 [[ounce]]s in an [[avoirdupois]] pound
-* There are 16 [[Pawn (chess)|pawns]] in a [[chess]] set and each player in a [[chess]] game starts with sixteen pieces
-[[Image:Muybridge race horse animated.gif|thumb|right|300px|Sixteen frames of images]]
-* [[The Sixteen]] is an English choir performing early religious music
-*In the video game ''[[No Man's Sky]]'', 16 is central to the plot as it is the number of minutes before the Atlas simulation resets.
-* [[Sixteen (band)|Sixteen]] is a Polish band that represented [[Poland]] in the [[1998 Eurovision Song Contest]]
-* The [[Cadillac Sixteen]]
-* There are 16 different personality types in the [[Myers–Briggs Type Indicator|Myers–Briggs]] classification system
-* A note played for one-sixteenth the duration of a [[whole note]] is called a [[sixteenth note]] or a semiquaver
-* In the [[16-bit era]], [[16-bit]] microprocessor ran [[16-bit application]]s
-* [[Sixteen Kingdoms]], part of [[Chinese history]]
-* The fighter jet, the [[F-16 Fighting Falcon]]
-* [[16 mm]] film was originally an amateur [[movie]] format, but is now used by professionals
-* "[[16 (Green Day song)|16]]" is a song by American band [[Green Day]]
-* The [[M16 rifle]]
-* The number 16 is the symbol of the [[A Day of Solidarity with Belarus|Day of solidarity with political prisoners and victims of the Lukashenka regime in Belarus]], which is commemorated on 16th of every months by demonstrations and flash mobs worldwide{{citation needed|date=May 2018}}
-* A sixteen is a slang term for a verse in a hip hop song, which are often written in 16-[[Bar (music)|bar]] [[stanza]]s.<ref>{{cite web|url=http://artsedge.kennedy-center.org/content/3656/|title=ARTSEDGE: The Poetics of Hip-Hop|first=The Kennedy Center|last=ArtsEdge|website=artsedge.kennedy-center.org|access-date=21 March 2018|archive-date=5 January 2007|archive-url=https://web.archive.org/web/20070105200646/http://artsedge.kennedy-center.org/content/3656/|url-status=dead}}</ref>
-* [[List of Dragon Ball characters#Android #16|Android 16]], a fictional character in the ''Dragon Ball'' manga and anime series
-* The amount of waking hours in a day in an "8 hours of sleep" schedule
-* In the story of the [[Sleeping Beauty]] to Walt Disney, a spell is placed on the princess Aurora that when she reaches her 16th birthday, she will "prick her finger on the spindle of a spinning wheel and die"
-* 16 is the number of the French department [[Charente]]
-* Many [[bank card number]]s are 16 digits long
-* There is a [[No Doubt]] song titled "Sixteen" on the album ''[[Tragic Kingdom]]''
-* The [[metalcore]] band [[Demon Hunter (band)|Demon Hunter]] has a song titled "Sixteen" on their ''[[Storm the Gates of Hell]]'' album
-* In [[Belgium]], 16 is colloquially used to refer to the Belgian government or Prime Minister, especially in media, because of the official seat of the Belgian federal government being located on 16, rue de la Loi in Brussels. The full address is also sometimes used, in a similar way as 10, Downing Street in England.<ref>{{cite web |url=http://chancellerie.belgium.be/fr/content/le-16 |title=Le "16" &#124; Chancellerie du Premier Ministre |access-date=9 June 2015 |archive-url=https://web.archive.org/web/20150704060938/http://chancellerie.belgium.be/fr/content/le-16 |archive-date=4 July 2015 |url-status=dead  }}</ref>{{failed verification|reason=That shows the building is referred to as "the 16", not the government|date=July 2015}}
-* The number of rays in the [[Vergina Sun]], symbol by Philip's Argead dynasty, possible religious symbol representing the Olympian gods.
-* There are sixteen petals on the [[Imperial Seal of Japan]].
-* There were sixteen lands created by Ahura Mazda, according to [[Avestan geography]], which were then followed by sixteen negative counter-creations of Angra Mainyu.
 ==References==