48 (number)

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← 47 48 49 →
Cardinal forty-eight
Ordinal 48th
(forty-eighth)
Factorization 24× 3
Divisors 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Greek numeral ΜΗ´
Roman numeral XLVIII
Binary 1100002
Ternary 12103
Quaternary 3004
Quinary 1435
Senary 1206
Octal 608
Duodecimal 4012
Hexadecimal 3016
Vigesimal 2820
Base 36 1C36

48 (forty-eight) is the natural number following 47 and preceding 49. It is one third of a gross, or four dozens.

In mathematics[edit]

Forty-eight is the double factorial of 6,[1] a highly composite number.[2] Like all other multiples of 6, it is a semiperfect number.[3] 48 is the second 17-gonal number.[4]

48 is the smallest number with exactly ten divisors.

There are 11 solutions to the equation φ(x) = 48, namely 65, 104, 105, 112, 130, 140, 144, 156, 168, 180 and 210. This is more than any integer below 48, making 48 a highly totient number.[5]

Since the greatest prime factor of 482 + 1 = 2305 is 461, which is clearly more than twice 48, 48 is a Størmer number.[6]

48 is a Harshad number in base 10.[7] It has 24, 2, 12, and 4 as factors.

In science[edit]

Astronomy[edit]

In religion[edit]

In music[edit]

  • 48 is twice the total number of major and minor keys in Western tonal music (twenty-four), not counting enharmonic equivalents.
  • Johann Sebastian Bach's Well-Tempered Clavier is informally known as The Forty-Eight because it consists of a prelude and a fugue in each major and minor key, for a total of forty-eight pieces.
  • "48" is a song by Sunny Day Real Estate
  • "48" is a song by Tyler, The Creator
  • "Forty eight" is a song by Truckfighters on their 2007 album, Phi
  • "48 Hour Parole" is a song by the Hollies
  • "48 Crash" is a song by Suzi Quatro
  • Familiar 48 is an alternative pop/rock band formerly known as Bonehead
  • On Tool’s album Ænima, there is a song named "Forty-Six & 2"; the sum of which is 48.
  • AKB48 Group is a Japanese idol girl band

In sports[edit]

In other fields[edit]

Forty-eight may also refer to:

References[edit]

  1. ^ "Sloane's A000165 : Double factorials". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30. 
  2. ^ "Sloane's A002182 : Highly composite numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30. 
  3. ^ "Sloane's A005835 : Pseudoperfect (or semiperfect) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30. 
  4. ^ "Sloane's A051869 : 17-gonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30. 
  5. ^ "Sloane's A097942 : Highly totient numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30. 
  6. ^ "Sloane's A005528 : Størmer numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30. 
  7. ^ "Sloane's A005349 : Niven (or Harshad) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30. 
  8. ^ [1]