16 (number)

"XVI" redirects here. For other uses, see 16 (disambiguation).

← 15 16 17 →
← 10 11 12 13 14 15 16 17 18 19 → List of numbers Integers ← 0 10 20 30 40 50 60 70 80 90 →
Cardinal	sixteen
Ordinal	16th (sixteenth)
Numeral system	hexadecimal
Factorization	24
Divisors	1, 2, 4, 8, 16
Greek numeral	ΙϚ´
Roman numeral	XVI
Binary	100002
Ternary	1213
Senary	246
Octal	208
Duodecimal	1412
Hexadecimal	1016
Hebrew numeral	ט"ז / י"ו
Babylonian numeral	𒌋𒐚

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: 4 ² = 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 (${\displaystyle m=4}$, ${\displaystyle n=2}$, or vice versa). ^[1] It has this property because ${\displaystyle 2^{2}=2\times 2}$. 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 ${\displaystyle 2^{n}+1}$ 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 ${\displaystyle 4^{2}}$ being equal to ${\displaystyle 4\times 4.}$

Hexadecimal

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

Science

Chemistry

Group 16 of the periodic table are the chalcogens. 16 is the atomic number of sulfur.

Psychology

• There are 16 different personality types in the Myers–Briggs classification system.
• The amount of waking hours in a day in an "8 hours of sleep" schedule is 16

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. The British have 16 ounces in one pound; the Chinese used to have 16 liangs in one jin. In old days^{[ vague ]}, 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.

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. ^{[4] [5]} 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.

Other fields

• Many bank card numbers are 16 digits long.
• There are 16 pawns in a chess set and each player in a chess game starts with sixteen pieces.

References

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.). "SequenceA000112(Number of partially ordered sets (posets) with n unlabeled elements)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
4. "Age of Consent By State". Archived from the original on 17 April 2011.
5. "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.