|Factorization||3 × 7|
|Divisors||1, 3, 7, 21|
- 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.
- an octagonal number.
- a composite number, its proper divisors being 1, 3 and 7.
- the sum of the first six natural numbers (1 + 2 + 3 + 4 + 5 + 6 = 21), making it a triangular number.
- 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 (1114).
- 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.
Note that a necessary condition for n is that for any a coprime to n, a and n - a must satisfy the condition above, therefore at least one of a and n - a must only have factor 2 and 5.
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
so fails to hold when n > 273 (actually, when n > 33).
Just check a few numbers to see that n = 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 15, 21.
|Look up twenty-one in Wiktionary, the free dictionary.|
- In several countries 21 is the age of majority. See also: Coming of age.
- In all US states, 21 is the drinking age.
- However, in Puerto Rico and U.S. Virgin Islands, the drinking age is 18.
- In California, Hawaii, New York, and New Jersey, 21 is the minimum age that one person may purchase cigarettes and other tobacco products.
- In some countries it is the voting age.
- 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 most US states, 21 is the minimum age at which a person may gamble or enter casinos.
- In 2011, Adele named her second studio album 21, because of her age at the time.
- 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 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
- 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
- 21 Guns, a 2009 song by the punk-rock band Green Day
- 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 (the military profile designation granting an exemption from the military service)
- 21 grams is the weight of the soul, according to research by Duncan MacDougall, generally regarded as meaningless.
- The number of the French department Côte-d'Or
- The key value and highest-winning point total of the popular casino game Blackjack
- The number of shillings in a guinea.
- The number of solar rays in the flag of Kurdistan.
|Wikimedia Commons has media related to 21 (number).|
- "Sloane's A016105 : Blum integers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
- "Sloane's A000045 : Fibonacci numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
- "Sloane's A005349 : Niven (or Harshad) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
- "Sloane's A001006 : Motzkin numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
- "Sloane's A000217 : Triangular numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
- "Sloane's A000567 : Octagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
- 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.
- "Sloane's A000931 : Padovan sequence". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.