# 45 (number)

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

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 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.

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).

## In other fields

Forty-five may also refer to:

## References

1. ^ Sloane, N.J.A. (ed.). "Sequence A000217 (Triangular numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
2. ^ Sloane, N.J.A. (ed.). "Sequence A000384 (Hexagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
3. ^ Sloane, N.J.A. (ed.). "Sequence A051868 (16-gonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
4. ^ Sloane, N.J.A. (ed.). "Sequence A005528 (Størmer numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
5. ^ Sloane, N.J.A. (ed.). "Sequence A006886 (Kaprekar numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
6. ^ Sloane, N.J.A. (ed.). "Sequence 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