45 (number)

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← 44 45 46 →
Cardinal forty-five
Ordinal 45th
(forty-fifth)
Factorization 32× 5
Divisors 1, 3, 5, 9, 15, 45
Roman numeral XLV
Binary 1011012
Ternary 12003
Quaternary 2314
Quinary 1405
Senary 1136
Octal 558
Duodecimal 3912
Hexadecimal 2D16
Vigesimal 2520
Base 36 1936

45 (forty-five) is the natural number that succeeds 44 and precedes 46.

In mathematics[edit]

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[edit]

Astronomy[edit]

In music[edit]

In other fields[edit]

Forty-five may also refer to:

References[edit]

  1. ^ "Sloane's A000217 : Triangular numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30. 
  2. ^ "Sloane's A000384 : Hexagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30. 
  3. ^ "Sloane's A051868 : 16-gonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30. 
  4. ^ "Sloane's A005528 : Størmer numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30. 
  5. ^ "Sloane's A006886 : Kaprekar numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30. 
  6. ^ "Sloane's A005349 : Niven (or Harshad) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30. 
  7. ^ Arthur Hill Cash (2007), John Wilkes: The Scandalous Father of Civil Liberty, Yale University Press, p. 219, ISBN 978-0-300-12363-0