16 (number)

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← 15
17 →
16
Cardinal sixteen
Ordinal 16th
(sixteenth)
Numeral system hexadecimal
Factorization 24
Divisors 1, 2, 4, 8, 16
Roman numeral XVI
Binary 10000
Octal 20
Duodecimal 14
Hexadecimal 10
Hebrew ט"ז (Tet Zayin)
"Sixteen" redirects here. For other uses, see Sixteen (disambiguation)


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Sixteen is a composite number, and a square number, being 42 = 4 × 4. It is the tiniest number with exactly five divisors, its proper divisors being 1, 2, 4 and 8. 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). It is the fourth power of two. For this reason, 16 was used in weighing light objects in several cultures. The British used to have 16 ounces in one pound, the Chinese used to have 16 langs 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 5's and 5 lower beads to represent the 1's, the 7 beads can represent from a hexadecimal digit from 0 to 15 in each column.

Sixteen is the only integer that equals mn and nm, for some unequal integral m and n (m=4, n=2, or vice versa). It has this property because 2^2=2\times2. It is also equal to 2↑↑3, (using Knuth's up-arrow notation).

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 member shares a factor with either the first or the last member, 16 is an Erdős–Woods number. The smallest such range of 16 consecutive integers is from 2184 to 2200.[1]

16 is a centered pentagonal number.

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

Contents

[edit] In science

[edit] Age 16

  • Sixteen is the minimum age for being allowed an official beginners driver's license with parental consent in many U.S. states and in Canada. In Australia and Norway it is the age one can begin to get a learner's licence.
  • Sixteen is the minimum age for getting an adult job in most states and provinces (as well as dropping out of school).
  • In the United States, female sixteen year olds earn the right to privacy laws surrounding OBGYN practices.
  • In the Netherlands it is the legal minimum age for a person to purchase any tobacco product.
  • Sixteen is the age of consent for many jurisdictions around the world.
  • For its "coming of age" significance, this age has inspired the titles of many songs, such as "Happy Birthday Sweet Sixteen", "You're Sixteen", "Sweet Sixteen", "Sweet Little Sixteen" and "Sixteen Candles", the last of which was borrowed as the title of a John Hughes movie. (This last one was also parodied in a novelty song by The Mothers, titled "Eddie Are You Kidding?", a tribute to the Los Angeles clothing store Zachary All; the tag line is "Sixteen Tailors...")
  • Sixteen is the minimum age to get married with parental consent in many countries.
  • Sixteen is the legal drinking age in France, Germany, Belgium, Austria, The Philippines, The Netherlands and Portugal.
  • In The Netherlands sixteen is the age when all adult rights are granted but the age of majority is 18.
  • 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 U.S.

[edit] In sports

[edit] Football

[edit] Baseball

[edit] Hockey

  • Also, not used by any Detroit Red Wing player, in honor of Vladimir Konstantinov.

[edit] In other fields

Sixteen frames of images
Sixteen frames of images

[edit] References

  1. ^ R. K. Guy, Unsolved Problems in Number Theory New York: Springer-Verlag (2004): B28
  2. ^ Lesson plan explaining the reasoning behind the hip-hop slang "sixteen"