# 45 (number)

__: Natural number__

**Short description**
| ||||
---|---|---|---|---|

Cardinal | forty-five | |||

Ordinal | 45th (forty-fifth) | |||

Factorization | 3^{2} × 5 | |||

Divisors | 1, 3, 5, 9, 15, 45 | |||

Greek numeral | ΜΕ´ | |||

Roman numeral | XLV | |||

Binary | 101101_{2} | |||

Ternary | 1200_{3} | |||

Quaternary | 231_{4} | |||

Quinary | 140_{5} | |||

Senary | 113_{6} | |||

Octal | 55_{8} | |||

Duodecimal | 39_{12} | |||

Hexadecimal | 2D_{16} | |||

Vigesimal | 25_{20} | |||

Base 36 | 19_{36} |

**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 *p*^{2}*q*, with *p* and *q* being prime.

Since the greatest prime factor of 45^{2} + 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 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

- 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.

## See also

- List of highways numbered 45

## References

- ↑ Sloane, N. J. A., ed. "Sequence A000217 (Triangular numbers)". OEIS Foundation. https://oeis.org/A000217. Retrieved 2016-05-30.
- ↑ Sloane, N. J. A., ed. "Sequence A000384 (Hexagonal numbers)". OEIS Foundation. https://oeis.org/A000384. Retrieved 2016-05-30.
- ↑ Sloane, N. J. A., ed. "Sequence A051868 (16-gonal numbers)". OEIS Foundation. https://oeis.org/A051868. Retrieved 2016-05-30.
- ↑ Sloane, N. J. A., ed. "Sequence A005528 (Størmer numbers)". OEIS Foundation. https://oeis.org/A005528. Retrieved 2016-05-30.
- ↑ Sloane, N. J. A., ed. "Sequence A006886 (Kaprekar numbers)". OEIS Foundation. https://oeis.org/A006886. Retrieved 2016-05-30.
- ↑ Sloane, N. J. A., ed. "Sequence A005349 (Niven (or Harshad) numbers)". OEIS Foundation. https://oeis.org/A005349. Retrieved 2016-05-30.
- ↑ Sloane, N. J. A., ed. "Sequence A006872". OEIS Foundation. https://oeis.org/A006872.
- ↑ Arthur Hill Cash (2007),
*John Wilkes: The Scandalous Father of Civil Liberty*, Yale University Press, p. 219, ISBN 978-0-300-12363-0, https://archive.org/details/johnwilkes00arth_0/page/219

Original source: https://en.wikipedia.org/wiki/45 (number).
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