16 (number)

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"Sixteen" and "XVI" redirect here. For other uses, see 16 (disambiguation).
← 15 16 17 →
Cardinal sixteen
Ordinal 16th
Numeral system hexadecimal
Factorization 24
Divisors 1, 2, 4, 8, 16
Roman numeral XVI
Binary 100002
Ternary 1213
Quaternary 1004
Quinary 315
Senary 246
Octal 208
Duodecimal 1412
Hexadecimal 1016
Vigesimal G20
Base 36 G36
Hebrew ט"ז (Tet Zayin)

16 (sixteen) is the natural number following 15 and preceding 17. 16 is a composite number, and a square number, being 42 = 4 × 4. It is the smallest number with exactly five divisors, its proper divisors being 1, 2, 4 and 8.

In speech, the numbers 16 and 60 are often confused. When carefully enunciated, they differ in which syllable is stressed: 16 /sɪksˈtn/ vs 60 /ˈsɪksti/. However, in dates such as 1666 or when contrasting numbers in the teens, such as 15, 16, 17, the stress shifts to the first syllable: 16 /ˈsɪkstn/.

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, 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. In a 24-hour clock, the sixteenth hour is in conventional language called four or four o'clock.

In mathematics[edit]

As a power of 2 it has an aliquot sum one less than itself, 15; and is the fifth composite member of the 3-aliquot tree having the 7 member aliquot sequence (16, 15, 9, 4, 3, 1, 0).

Sixteen is the first number to be the aliquot sum of a lesser number, 12; it is also the aliquot sum of the greater number; the discrete semiprime, 26. It is the fourth power of two.

Sixteen is the only integer that equals mn and nm, for some unequal integers m and n (m = 4, n = 2, or vice versa).[1] It has this property because 22 = 2 × 2. It is also equal to 32 (see tetration).

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

Since it is possible to find sequences of 16 consecutive integers such that each inner member shares a factor with either the first or the last member, 16 is an Erdős–Woods number.[2] The smallest such range of 16 consecutive integers is from 2184 to 2200.[3]

In bases 20, 24 and 30, sixteen is a 1-automorphic number (displayed as the numeral 'G').

16 is a centered pentagonal number.[4]

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

16 appears in the Padovan sequence, preceded by the terms 7, 9, 12 (it is the sum of the first two of these).[5]

In science[edit]

In languages[edit]


In Spanish and Portuguese, 16 is the first compound number (Spanish: dieciséis, European Portuguese: dezasseis, Brazilian Portuguese: dezesseis); the numbers 11 (Spanish: once, Portuguese: onze) through 15 (Spanish: quince, Portuguese: quinze) have their own names.

Age 16[edit]

  • Sixteen is the minimum age for being allowed an official beginner's driver's license with parental consent in many U.S. states and in Canada. In Australia, Iceland, New Zealand, Norway, South Africa, and the Isle of Man, it is the age one can begin to get a learner's license.
  • A "sweet sixteen" is celebrated by many 16-year-old girls in the United States. It is a coming of age celebration that traditionally marks a girl's transition into womanhood. For its significance, this "coming of age" has inspired the titles of many songs, such as "Happy Birthday Sweet Sixteen", "You're Sixteen", "Sweet Sixteen", "U16 Girls" "Sweet Little Sixteen" and "Sixteen Candles"
  • In some states in the U.S., and all provinces in Canada, excluding Alberta and Saskatchewan, 16 is the age one can obtain a learner's permit to learn to drive a motor vehicle
  • Sixteen is the minimum age for getting an adult job[clarification needed] in most states and provinces across the globe[citation needed]
  • Sixteen is the minimum age that one can drop out of school in many states of the United States and Canada (however, restrictions apply and vary depending on state or province)[6]
  • In the United States, female 16-year-olds earn the right to privacy laws surrounding OBGYN practices
  • In Belgium, Switzerland and Italy, it is the legal minimum age for a person to purchase any tobacco product
  • In the United States and Canada, 16 is the most common age of sexual consent, as well as in the United Kingdom.[7][8]
  • 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, Italy and Portugal
  • Minimum age at which one can buy, rent, purchase, buy tickets to, or view a 16+ rated movie in the 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 states
  • Minimum age at which one can obtain a 10-year passport in the United States, United Kingdom, and Australia
  • Minimum age at which one can join the Armed Forces in the United Kingdom (deployment is only allowed at 18)
  • Voting age in Argentina, Austria, Brazil, Cuba, Ecuador, the Isle of Man and Nicaragua, and during the 19th century, in the Transvaal Republic

In sports[edit]

American football[edit]

  • The number of regular-season games that each NFL team currently plays

Association football[edit]

  • The number of teams that qualified for the finals of the FIFA World Cup from 1934 through 1978 (although for various reasons, only 15 competed in the 1938 and 1950 finals)
  • The number of teams that qualified for the finals of the FIFA Women's World Cup from 1999 through 2011

Auto racing[edit]

  • The number of a car in the NASCAR Sprint Cup Series. Run by Roush Fenway Racing and its predecessor, Roush Racing, from 1992–2000 and 2002–present. Since the car's return to the Cup Series, it has been driven by Greg Biffle.
  • As of the 2014 season, the number of drivers that qualify for NASCAR's season-ending Chase for the Sprint Cup.


Rugby union[edit]

  • Since adopting its current 15-team format in 2011, Super Rugby has conducted a 16-game regular season.

Multiple sports[edit]

In other fields[edit]

  • 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 ounces in an avoirdupois pound
  • There are 16 pawns in a chess set and each player in a chess game starts with sixteen pieces
Sixteen frames of images


  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 2016-06-01. 
  3. ^ R. K. Guy, Unsolved Problems in Number Theory New York: Springer-Verlag (2004): B28
  4. ^ "Sloane's A005891 : Centered pentagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01. 
  5. ^ "Sloane's A000931 : Padovan sequence". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01. 
  6. ^ Mikulecky, Marga (April 2013). "Compulsory School Age Requirements" (PDF). Education Commission of the States. Retrieved January 8, 2015. 
  7. ^ "Age Of Consent By State". 
  8. ^ "Age of consent for sexual intercourse". 
  9. ^ Lesson plan explaining the reasoning behind the hip-hop slang "sixteen"
  10. ^ http://chancellerie.belgium.be/fr/content/le-16

External links[edit]