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21 (number)

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← 20 21 22 →
Cardinaltwenty-one
Ordinalst
Factorization
Divisors1, 3, 7, 21
Greek numeralΚΑ´
Roman numeralXXI
Binary101012
Ternary2103
Senary336
Octal258
Duodecimal1912
Hexadecimal1516

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

In mathematics

Twenty-one is a Fibonacci number, a Harshad number, a Motzkin number, a triangular number and an octagonal number, as well as a composite number, its proper divisors being 1, 3 and 7.

21 is the sum of the first six integers (1+2+3+4+5+6=21).

21 is the fifth discrete bi-prime and the second in the (3.q) family. With 22 it forms the second discrete bi-prime pair. As it is a semiprime with both its prime factors being Gaussian primes, 21 is then a Blum integer.

21 has an aliquot sum of 11 though it is the second composite number found in the 11-aliquot tree with the abundant 18 being the first such member. Twenty-one is the first number to be the aliquot sum of three numbers 18, 51, 91.

21 appears in the Padovan sequence, preceded by the terms 9, 12, 16 (it is the sum of the first two of these).

The sum of divisors for the integers 1 through 6 is 21.

21 is a repdigit in base 4 (111).

21 is the smallest number of differently sized squares needed to square the square.[1]

In science

In music

Age 21

In sports

In other fields

21 is:

  • The current century—spanning the years from 2001 to 2100—referred to as the 21st century. The approach of this century inspired many forward-looking 20th century events and company and product names, such as the Century 21 Exposition (another name for the 1962 Seattle World's Fair), Century 21 Real Estate, and Century 21 Television (producers of Sylvia and Gerry Anderson Supermarionation shows like Thunderbirds and Captain Scarlet and the Mysterons).
  • The Twenty-first Amendment repealed the Eighteenth Amendment, thereby ending Prohibition.
  • Illinois - the 'Land of Lincoln' - is the 21st state to join the United States. Abraham Lincoln moved to Illinois when he was 21 and he met his future wife - Mary Todd - in Springield when she was 21. Illinois currently has 21 electoral votes in the US Presidential Election.
  • Pier 21 was, from 1928 to 1971, the place where immigrants entered Canada. It was called the "Gateway to Canada."
  • Forever 21 (also operating as XXI Forever) is a US-based chain of clothing stores that was founded in 1984.
  • The number of spots on a standard cubical dice (1+2+3+4+5+6)
  • The number of firings in a 21-gun salute honoring Royalty or leaders of countries
  • A card game, also called vingt-et-un (French for "twenty-one"), pontoon, or blackjack
  • There are 21 trump cards of the tarot deck if one does not consider the fool to be a proper trump card.
  • Twenty One, a TV quiz show that ran from 1956 to 1958, most remembered for the scandal that the wins were fixed (see Quiz show scandals). It was remade in 2000.
  • The title of at least four different movies:
A 1918 comedy starring Bryant Washburn and Gertrude Selby
A 1923 drama starring Richard Barthelmess and Dorothy Mackaill
A 1991 drama starring Patsy Kensit
A 2008 drama starring Kevin Spacey, Laurence Fishburne, and Kate Bosworth, based on the book Bringing Down the House.

Historical years

21 A.D., 21 B.C., 1921, 2021, etc.

References

  1. ^ 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.