# 16 (number): Map

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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 , , and .

In speech, the numbers 16 and 60 are often confused. When carefully enunciated, they differ in which syllable is stressed: 16 vs 60 . 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 .

Sixteen 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 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 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.

## In mathematics

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 second number to be the aliquot sum of a lesser number; 12, it is also the aliquot sum of the greater discrete biprime 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). 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 not possible to find sequences of 16 consecutive integers such that each inner member member shares a factor with either the first or the first member, 16 is an Erdős–Woods number. The smallest such range of 16 consecutive integers is from 2184 to 2200.

16 is a centered pentagonal number.

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).

## In sports

### Hockey

• The number 16 is retired by the Philadelphia Flyers in honor of Bobby Clarke.

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

### Auto Racing

• Greg Biffle is currently the driver of the number 16 car in the NASCAR Sprint Cup Series.

## In other fields ## 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"

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