45 (number)

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

 ← 44 45 46 →
Cardinalforty-five
Ordinal45th
(forty-fifth)
Factorization32× 5
Divisors1, 3, 5, 9, 15, 45
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). It is the smallest triangle number (after 1) which can be written as the sum of two squares. It is also a hexagonal and 16-gonal number,

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 clearly more than 45 twice, 45 is a Størmer number.

In base 10, it is a Kaprekar number, and a Harshad number.

In other fields

Forty-five may also refer to:

• +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
• 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.[1]
• In the wake of the Scottish independence referendum, 2014, the number 45 came to represent the percentage of people who voted yes. The phrase "we are the 45" can be seen on social media, where it is used by supporters of an independant Scotland.

References

1. ^ Arthur Hill Cash (2007), John Wilkes: The Scandalous Father of Civil Liberty, Yale University Press, p. 219, ISBN 978-0-300-12363-0