# 45 (number)

Short description: Natural number
 ← 44 45 46 →
Cardinalforty-five
Ordinal45th
(forty-fifth)
Factorization32 × 5
Divisors1, 3, 5, 9, 15, 45
Greek numeralΜΕ´
Roman numeralXLV
Binary1011012
Ternary12003
Quaternary2314
Quinary1405
Senary1136
Octal558
Duodecimal3912
Vigesimal2520
Base 361936

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

45 is conjectured R(5, 5) (sequence A120414 in the OEIS).

45 is a little Schroeder number.

φ(45) = φ(σ(45)).[7]

## 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.[8]
• 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.