45 (number)
45 (forty-five) is the natural number following 44 and followed by 46.
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| Cardinal | forty-five | |||
| Ordinal | 45th (forty-fifth) | |||
| Factorization | 32 × 5 | |||
| Divisors | 1, 3, 5, 9, 15, 45 | |||
| Greek numeral | ΜΕ´ | |||
| Roman numeral | XLV | |||
| Binary | 1011012 | |||
| Ternary | 12003 | |||
| Octal | 558 | |||
| Duodecimal | 3912 | |||
| Hexadecimal | 2D16 | |||
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).[1] It is the second smallest triangle number (after 1 and 10) which can be written as the sum of two squares. It is also a hexagonal[2] and 16-gonal number.[3]
45 is the sixth positive integer with a prime factorization of the form p2q, with p and q being prime.
Since the greatest prime factor of 452 + 1 = 2026 is 1013, which is much more than 45 twice, 45 is a Størmer number.[4]
In base 10, it is a Kaprekar number[5] and a Harshad number.[6]
45 is the smallest odd number that has more divisors than n+1 (sequence A138171 in the OEIS) and that has a larger sum of divisors than n+1 (sequence A067828 in the OEIS).
In science
- The atomic number of rhodium
Astronomy
- Messier object M45, a magnitude 1.4 open cluster in the constellation Taurus, also known as the Pleiades
- The New General Catalogue object NGC 45, a magnitude 10.6 spiral galaxy in the constellation Cetus
In music
45 rpm gramophone record
- A type of gramophone record classified by its rotational speed of 45 revolutions per minute (rpm)
- The group Stars on 45 and its self-titled 1981 song, "Stars on 45"
- "45 and Fat", a 1996 song by Babybird
- "Forty-Five", the title of a 2000 song by The Atomic Bitchwax
- "45", the title of a 2002 song by Elvis Costello, both referring to the 45 rpm singles and to the artist's age when he wrote the song.
- "45", the title of a 2012 song by The Gaslight Anthem
- "45", the title of a 2006 song by noodles
- "45", the title of a 2007 song by The Saturday Knights
- "45", the title of a 2003 song by Shinedown
- 45, the title of a 1982 album by Kino
- "Do the 45", the title of a 2007 song by Ryan Shaw
- forty-five is repeated continuously in the lyrics of the 1997 song "Brimful of Asha" by Cornershop
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.
- The number of the French department Loiret.
- The maximum mark an International Baccalaureate student can obtain.
- 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.[7]
- The number of the laps of the German Grand Prix from 1978 until 2001 (except 1985 because the race was held at Nürburgring).
- Donald Trump, 45th President of the United States.
See also
References
- Sloane, N. J. A. (ed.). "Sequence A000217 (Triangular numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
- Sloane, N. J. A. (ed.). "Sequence A000384 (Hexagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
- Sloane, N. J. A. (ed.). "Sequence A051868 (16-gonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
- Sloane, N. J. A. (ed.). "Sequence A005528 (Størmer numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
- Sloane, N. J. A. (ed.). "Sequence A006886 (Kaprekar numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
- Sloane, N. J. A. (ed.). "Sequence A005349 (Niven (or Harshad) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
- Arthur Hill Cash (2007), John Wilkes: The Scandalous Father of Civil Liberty, Yale University Press, p. 219, ISBN 978-0-300-12363-0
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