45 (number)

45 (forty-five) is the natural number following 44 and followed by 46.

In mathematics

Forty-five is the smallest odd number that has more divisors than $n+1$, and that has a larger sum of divisors than $n+1$. It is the sixth positive integer with a prime factorization of the form $p^q$, with and being prime.

Forty-five is the sum of all single-digit decimal digits: $0+1+2+3+4+5+6+7+8+9=45$. It is, equivalently, the ninth triangle number.

Forty-five is also the fourth hexagonal number and the second hexadecagonal number, or 16-gonal number. It is also the second smallest triangle number (after 1 and 10) that can be written as the sum of two squares.

Since the greatest prime factor of $45^+1=2026$ is 1,013, which is much more than 45 twice, 45 is a Størmer number. In decimal, 45 is a Kaprekar number and a Harshad number.

Forty-five is a little Schroeder number; the next such number is 197, which is the 45th prime number.

Forty-five is conjectured from Ramsey numbers $R(5, 5)$.

$\phi(45)=\phi(\sigma(45))$

If the Tits group is included as a ''nonstrict'' group of Lie type, then there are 45 finite simple groups.

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 music

* 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
* 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.
*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

* List of highways numbered 45

References

{{Integers, zero

Integers