21 (number)
21 is the natural number following 20 and preceding 22.
In mathematics
21 is:- a Blum integer, since it is a semiprime with both its prime factors being Gaussian primes.
- a Fibonacci number.
- a Harshad number.
- a Motzkin number.
- a triangular number, because it is the sum of the first six natural numbers.
- an octagonal number.
- a composite number, its proper divisors being 1, 3 and 7.
- the sum of the divisors of the first 5 positive integers.
- the smallest non-trivial example of a Fibonacci number whose digits are Fibonacci numbers and whose digit sum is also a Fibonacci number.
- a repdigit in base 4.
- the smallest natural number that is not close to a power of 2, 2n, where the range of closeness is ±n.
- the smallest number of differently sized squares needed to square the square.
- the largest n with this property: for any positive integers a,b such that a + b = n, at least one of and is a terminating decimal. See a brief proof below.
Let donate the quantity of the numbers smaller than n that only have factor 2 and 5 and that are coprime to n, we instantly have.
We can easily see that for sufficiently large n,, but, as n goes to infinity, thus fails to hold for sufficiently large n.
In fact, For every n > 2, we have
and
so fails to hold when n > 273.
Just check a few numbers to see that n = 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 15, 21.
21 appears in the Padovan sequence, preceded by the terms 9, 12, 16.
In science
- The atomic number of scandium.
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 most US states, 21 is the minimum age at which a person may gamble or enter casinos.
- In the United States, 21 is the minimum age to purchase a handgun or handgun ammunition.
- In the United States, 21 is the age at which one can purchase multiple tickets to an R-rated film without providing identification. It is also the age to accompany one under the age of 17 as their parent or adult guardian for an R-rated movie.
- In some countries, 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 2011, Adele named her second studio album 21, because of her age at the time.
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 ; 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, 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.
In other fields
- The Twenty-first Amendment repealed the Eighteenth Amendment, thereby ending Prohibition.
- The number of spots on a standard cubical die
- The number of firings in a 21-gun salute honoring Royalty or leaders of countries
- 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 Chinese 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
- 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, 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.
- The number on the logo for the American game show Catch 21