48 (number)

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

47 48 49
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Cardinalforty-eight
Ordinal48th
(forty-eighth)
Factorization24 × 3
Divisors1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Greek numeralΜΗ´
Roman numeralXLVIII
Binary1100002
Ternary12103
Octal608
Duodecimal4012
Hexadecimal3016

In mathematics

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

Astronomy

In religion

  • The prophecies of 48 Jewish prophets and 7 prophetesses [8] were recorded in the Tanakh for posterity.
  • According to the Mishnah, Torah wisdom is acquired via 48 ways (Pirkei Avoth 6:6).
  • In Buddhism, Amitabha Buddha had made 48 great vows and promises to provide ultimate salvation to countless beings through countless eons, with benefits said to be available merely by thinking about his name with Nianfo practice. He is thus hailed as "King of Buddhas" through such skillful compassion and became a popular and formal refuge figure in Pureland Buddhism.

In music

  • 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 female idol group.

In sports

  • 48 is the total number of minutes in a full NBA game.

In other fields

Forty-eight may also refer to:

See also

References

  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.
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