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48 (number)

48 is the natural number following 47 and preceding 49.

Cardinal forty-eight
Ordinal 48th (forty-eighth)
Factorization 2^4\cdot 3
Divisors 2, 3, 4, 6, 8, 12, 16, 24
Roman numeral XLVIII
Binary 0110000
Hexadecimal 30

In mathematics

Forty-eight is the double factorial of 6, four dozens, a highly composite number, a 17-gonal number and a Harshad number.

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.

In science

In astronomy,

Messier object M48, a magnitude 5.5 open cluster in the constellation Hydra
The New General Catalogue object NGC 48 , a barred spiral galaxy in the constellation Andromeda
The Saros number of the solar eclipse series which began on -1331 February 8 and ended on -15 April 9. The duration of Saros series 48 was 1316.2 years, and it contained 74 solar eclipses.
The Saros number of the lunar eclipse series which began on -1246 July 11 and ended on 124 October 11. The duration of Saros series 48 was 1370.3 years, and it contained 77 lunar eclipses.

In other fields

Forty-eight is also:

  • twice the total number of major and minor keys in the 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.
  • 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 hours in two days, and hence also part of the title of the movies 48 Hrs. and Another 48 Hrs., starring Eddie Murphy and Nick Nolte.
  • the years AD 48, 48 BC, or 1948.

Last updated: 05-24-2005 11:13:22
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