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21 (number)

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For other uses, see 21 (disambiguation).
20 21 22
Cardinal twenty-one
Ordinal 21st
Factorization 3 × 7
Divisors 1, 3, 7, 21
Roman numeral XXI
Binary 101012
Ternary 2103
Quaternary 1114
Quinary 415
Senary 336
Octal 258
Duodecimal 1912
Hexadecimal 1516
Vigesimal 1120
Base 36 L36

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

In mathematics[edit]

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

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 natural numbers (1 + 2 + 3 + 4 + 5 + 6 = 21), making it a triangular number.

21 has an aliquot sum of 11 though it is the second composite number found in the 11-aliquot tree with the abundant square prime 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 the smallest non-trivial example of a Fibonacci number whose digits are Fibonacci numbers and whose digit sum is also a Fibonacci number.

21 is a repdigit in base 4 (1114).

21 is the smallest natural number that is not close to a power of 2, 2n, where the range of closeness is ±n.

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

In science[edit]

Age 21[edit]

  • In several countries 21 is the age of majority. See also: Coming of age.
  • In all US states 21, is the drinking age.
  • In Hawaii and New York, 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. 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 states, 21 is the minimum age, persons may gamble or enter casinos.

In sports[edit]

Number 21 on the road bicycle of Ellen van Dijk at the Ronde van Drenthe.

In other fields[edit]

Building called "21" in Zlín, Czech Republic.
Detail of the building entrance

21 is:


  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.
  2. ^ "Article 9 Scoring" (PDF). 3x3 Rules of the Game. FIBA. January 13, 2012. Retrieved November 2, 2012.