45 (number)

 ← 44 45 46 →
Cardinal forty-five
Ordinal 45th
(forty-fifth)
Factorization 32× 5
Divisors 1, 3, 5, 9, 15, 45
Roman numeral XLV
Binary 1011012
Ternary 12003
Quaternary 2314
Quinary 1405
Senary 1136
Octal 558
Duodecimal 3912
Vigesimal 2520
Base 36 1936

45 (forty-five) is the natural number that succeeds 44 and precedes 46.

In mathematics

Forty-five is a triangular number, and in particular the sum of all the decimal digits (0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45). It is the smallest triangle number (after 1) which can be written as the sum of two squares. It is also a hexagonal and 16-gonal number,

45 is the sixth positive integer with a prime factorization of the form p2q, with p and q being prime.

33 is the aliquot sum of 45 and the aliquot sequence of 45 is (45, 33, 15, 9, 4, 3, 1, 0).

Since the greatest prime factor of 452 + 1 = 2026 is 1013, which is clearly more than 45 twice, 45 is a Størmer number.

In base 10, it is a Kaprekar number and a Harshad number.

In other fields

Forty-five may also refer to:

• The '45 refers to the Jacobite rising of 1745 in Great Britain], or the year that World War II ended, which was 1945.
• A card game: Forty-five
• .45 (film), a 2006 motion picture.
• +45 is the telephone dialing code for Denmark
• 45 (book), a book of essays by record producer Bill Drummond, derived both from the speed of a pop single and from his age when he finished writing it
• A football match consists of two periods of 45 minutes each.
• Guns or ammunition of .45 caliber. In the United States, "45" is often a reference to one of two specific .45 caliber cartridges— the .45 Colt or the .45 ACP.
• I-45 is the designation for a US interstate highway in Texas, connecting the major cities of Dallas and Houston; it is also the shortest "primary" interstate highway (one ending in 0 or 5)
• The number of the French department Loiret
• In years of marriage, the sapphire wedding anniversary.
• Forty Five (audio drama) a Big Finish 2008 audio play made for the forty fifth anniversary of the British science fiction television show Doctor Who.
• Issue 45 of The North Briton was thought to be seditious but its publisher, John Wilkes, was celebrated as a champion of liberty. The number 45 was used as a symbol of support for him. Banquets were held with a theme of 45 while many items were produced showing the number or featuring it in some way. For example, a wig was produced with 45 curls.[1]

References

1. ^ Arthur Hill Cash (2007), John Wilkes: The Scandalous Father of Civil Liberty, Yale University Press, p. 219, ISBN 978-0-300-12363-0