48 (number)

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

Cardinal 48
forty-eight
Ordinal 48th
forty-eighth
Factorization 2^4\cdot 3
Divisors 1, 2, 3, 4, 6, 8,
12, 16, 24, 48
Roman numeral XLVIII
Binary 110000
Duodecimal 40
Hexadecimal 30
Octal 60

Contents

[edit] In mathematics

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

48 is the first number of the form (24.q) and is in abundance having an aliquot sum of 76. It is the lowest composite number to fall into the 41-aliquot tree having the 7 aliquot number sequence,(48, 76 , 64, 63, 41, 1, 0). 48 is highly abundant with an aliquot sum 158% higher than itself.

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.

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

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

[edit] In science

[edit] Astronomy

[edit] In religion

[edit] 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 Hour Parole" is a song by the Hollies
  • Formerly known as Bonehead, Familiar 48 is an alternative pop/rock band
  • The jam band Phish has 48 albums to date.
  • On the band tool’s album, Ænima, there is a song named Forty-Six & 2; the sum of which is 48.
  • AKB48 is the name of a Japanese pop idol group that consists of approximately 48 members.

[edit] In sports

48 is the car number in NASCAR Nextel Cup series of Jimmie Johnson, winner of the 2006 Daytona 500 and Cup champion in 2006 and 2007. If you split his number into two you would get his teammate's number, Jeff Gordon, which also has twice as more championships as Johnson does. At the University of Michigan, 48 is the retired jersey number of Gerald Ford, who would be better known for his political career than as a star of the Michigan Wolverines football team.

[edit] In other fields

Forty-eight is:

  • the number of hours in two days, and hence also part of the title of the movies 48 Hrs. and Another 48 Hrs.
  • the code for international direct dial phone calls to Poland.
  • the model number of the HP-48 S/SX/G/GX/G+/GII
  • the number of Ohio state punter Jon Thoma.
  • the number of hours one has to make a film in the 48 Hour Film Project
  • the number of cards in a Pinochle or Hanafuda deck.
  • "48 Hours" is a TV show on CBS
  • The number of episodes of Space:1999.
  • Arizona is the 48th state in the Union
  • The "Continental" 48 states are also referred to as the Lower 48" and "48 contiguous states"
  • Howdy Doody had 48 freckles (there were only 48 states in the Union when it first aired in 1947)
  • 48 (1996 Novel) is a book written by James Herbert
  • The number 48 in ASCII is what you add to any single digit integer to convert to its ASCII value.
  • If programming, use modulus ten to break it into individual digits.
  • 48 is the number of chromosomes apes have.
  • In the "Potrzebie System of Weights and Measures" (Mad #33) by Donald Knuth, 48 things is one MAD. (49 things is one "Baker's MAD.")
  • MAC address uses 48-bit (6-byte)

[edit] In Anime

  • In Full Metal Alchemist, the Slicer Brothers are joined to a single suit of armor under the alias number 48 when guarding Laboratory Five.

[edit] Historical years

48 A.D., 48 B.C., 1948, 2048, etc.