# 21 (number)

__: Natural number__

**Short description**
| ||||
---|---|---|---|---|

Cardinal | twenty-one | |||

Ordinal | 21st (twenty-first) | |||

Factorization | 3 × 7 | |||

Divisors | 1, 3, 7, 21 | |||

Greek numeral | ΚΑ´ | |||

Roman numeral | XXI | |||

Binary | 10101_{2} | |||

Ternary | 210_{3} | |||

Quaternary | 111_{4} | |||

Quinary | 41_{5} | |||

Senary | 33_{6} | |||

Octal | 25_{8} | |||

Duodecimal | 19_{12} | |||

Hexadecimal | 15_{16} | |||

Vigesimal | 11_{20} | |||

Base 36 | L_{36} |

**21** (**twenty-one**) is the natural number following 20 and preceding 22.

The current century is the 21st century AD, under the Gregorian calendar.

## In mathematics

21 is:

- a composite number, its proper divisors being 1, 3 and 7, and a deficient number as the sum of these divisors is less than the number itself.
- a Fibonacci number as it is the sum of the preceding terms in the sequence, 8 and 13.
^{[1]} - the fifth Motzkin number.
^{[2]} - a triangular number,
^{[3]}because it is the sum of the first six natural numbers (1 + 2 + 3 + 4 + 5 + 6 = 21). - an octagonal number.
^{[4]} - a Padovan number, preceded by the terms 9, 12, 16 (it is the sum of the first two of these) in the padovan sequence.
^{[5]} - a Blum integer, since it is a semiprime with both its prime factors being Gaussian primes.
^{[6]} - the sum of the divisors of the first 5 positive integers (i.e., 1 + (1 + 2) + (1 + 3) + (1 + 2 + 4) + (1 + 5))
- the smallest non-trivial example of a Fibonacci number whose digits are Fibonacci numbers and whose digit sum is also a Fibonacci number.
- a Harshad number.
^{[7]}* a repdigit in base 4 (111_{4}). - the smallest natural number that is not close to a power of 2, 2
^{n}, where the range of closeness is ±*n*. - the smallest number of differently sized squares needed to square the square.
^{[8]} - the largest
*n*with this property: for any positive integers*a*,*b*such that*a*+*b*=*n*, at least one of [math]\displaystyle{ \tfrac{a}{b} }[/math] and [math]\displaystyle{ \tfrac{b}{a} }[/math] is a terminating decimal. See a brief proof below.

Note that a necessary condition for Let [math]\displaystyle{ A(n) }[/math] denote the quantity of the numbers smaller than We can easily see that for sufficiently large In fact, For every - [math]\displaystyle{ A\lt 1 + \log_2(n) + \frac{3 \log_5(n)}{2} + \frac{\log_2(n) \log_5(n)}{2} }[/math]
and - [math]\displaystyle{ \varphi(n) \gt \frac {n} {e^\gamma\; \log \log n + \frac {3} {\log \log n}} }[/math]
so [math]\displaystyle{ \frac{\varphi(n)}{2} \lt }[/math] fails to hold when Just check a few numbers to see that '= 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 15, 21. |

## In science

- The atomic number of scandium.
- It is very often the day of the solstices in both June and December, though the precise date varies by year.

## Age 21

- In thirteen countries, 21 is the age of majority. See also: Coming of age.
- In eight countries, 21 is the minimum age to purchase tobacco products.
- In seventeen countries, 21 is the drinking age.
- In nine countries, it is the voting age.
- In the United States:
- 21 is the minimum age at which a person may gamble or enter casinos in most states (since alcohol is usually provided).
- 21 is the minimum age to purchase a handgun or handgun ammunition under federal law.
- 21 is the age at which one can purchase multiple tickets to an R-rated film.
- In some states, 21 is the minimum age to accompany a learner driver, provided that the person supervising the learner has held a full driver license for a specified amount of time. See also: List of minimum driving ages.

## In sports

- Twenty-one is a variation of street basketball, in which each player, of which there can be any number, plays for himself only (i.e. not part of a team); the name comes from the requisite number of baskets.
- In three-on-three basketball games held under FIBA rules, branded as 3x3, the game ends by rule once either team has reached 21 points.
- In badminton, and table tennis (before 2001), 21 points are required to win a game.
- In AFL Women's, the top-level league of women's Australian rules football, each team is allowed a squad of 21 players (16 on the field and five interchanges).

## In other fields

**21** is:

- The Twenty-first Amendment repealed the Eighteenth Amendment, thereby ending Prohibition.
- The number of spots on a standard cubical (six-sided) die (1+2+3+4+5+6)
- The number of firings in a 21-gun salute honoring royalty or leaders of countries
- "Twenty One", a 1994 song by an Irish rock band The Cranberries
- "21 Guns", a 2009 song by the punk-rock band Green Day
- Twenty One Pilots, an American musical duo
- There are 21 trump cards of the tarot deck if one does not consider The Fool to be a proper trump card.
- The standard TCP/IP port number for FTP connection
- The Twenty-One Demands were a set of demands which were sent to the
*China*government by the Japanese government of Okuma Shigenobu in 1915 - 21 Demands of MKS led to the foundation of Solidarity in Poland.
- In Israel, the number is associated with the profile 21 (the military profile designation granting an exemption from the military service)
- Duncan MacDougall reported that 21 grams is the weight of the soul, according to an experiment.
- The number of the French department Côte-d'Or
- Twenty-One (card game), an ancient card game in which the key value and highest-winning point total is 21
- Blackjack, a modern version of Twenty-One played in casinos

- The number of shillings in a guinea.
- The number of solar rays in the flag of Kurdistan.
*Twenty-One*, an American game show that became the center of the 1950s quiz show scandals when it was shown to be rigged.- The number on the logo for the American game show
*Catch 21* - The total number of Bitcoin to be released is 21 million “[1]”
*Twenty-One*, a 1991 British-American drama film directed by Don Boyd and starring Patsy Kensit.

## References

- ↑ "Sloane's A000045 : Fibonacci numbers". OEIS Foundation. https://oeis.org/A000045.
- ↑ "Sloane's A001006 : Motzkin numbers". OEIS Foundation. https://oeis.org/A001006.
- ↑ "Sloane's A000217 : Triangular numbers". OEIS Foundation. https://oeis.org/A000217.
- ↑ "Sloane's A000567 : Octagonal numbers". OEIS Foundation. https://oeis.org/A000567.
- ↑ "Sloane's A000931 : Padovan sequence". OEIS Foundation. https://oeis.org/A000931.
- ↑ "Sloane's A016105 : Blum integers". OEIS Foundation. https://oeis.org/A016105.
- ↑ "Sloane's A005349 : Niven (or Harshad) numbers". OEIS Foundation. https://oeis.org/A005349.
- ↑ C. J. Bouwkamp, and A. J. W. Duijvestijn, "Catalogue of Simple Perfect Squared Squares of Orders 21 Through 25." Eindhoven University of Technology, Nov. 1992.

Original source: https://en.wikipedia.org/wiki/21 (number).
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