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21 (number)

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21
Cardinal twenty-one
Ordinal 21st
(twenty-first)
Factorization 3 \cdot 7
Divisors 1, 3, 7, 21
Roman numeral XXI
Binary 101012
Octal 258
Duodecimal 1912
Hexadecimal 1516

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

Contents

[edit] 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 5 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]

[edit] In science

[edit] In music

[edit] Age 21

[edit] In sports

[edit] In other fields

21 is:

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.

[edit] Historical years

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

[edit] 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.
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