45 (number)

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).^[1] It is the smallest triangle number (after 1) 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.

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 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]

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
• The Saros number of the solar eclipse series which began on −1436 March 30 and ended on −156 May 7. The duration of Saros series 45 was 1280.1 years, and it contained 72 solar eclipses.
• The Saros number of the lunar eclipse series which began on −1369 August 19 and ended on 182 March. The duration of Saros series 45 was 1550.6 years, and it contained 87 lunar eclipses.

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 1981 Stars on 45 (song)
• Included in the title of "45 and Fat", a 1996 song by Babybird
• The title of a 2000 song by The Atomic Bitchwax, "Forty-Five"
• The title of a 2002 song by Elvis Costello, "45", both referring to the 45 rpm singles and to the artist's age when he wrote the song, which was released when he was 47
• The title of a 2003 song by Shinedown, "45" see 45 (Shinedown song)
• The title of a 2006 song by noodles, "45"
• The title of a 2007 song by Ryan Shaw, "Do the 45"
• The title of a 2007 song by The Saturday Knights, "45"
• The title of a 1982 album by Kino, 45
• The title of a 2012 song by The Gaslight Anthem, "45"
• Repeated continuously in 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.
• 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
• 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]

References