48 (number)
Encyclopedia : 4 : 48 : 48N : 48 (number)
48 (forty-eight) is the natural number following 47 and preceding 49.
| 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 | 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.
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.
In science
- The atomic number of cadmium
- The number of Ptolemaic constellations
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 religion
- The prophecies of 48 Jewish prophets and 7 prophetesses [link] were recorded in the Tanakh for posterity
- According to the Mishnah, Torah wisdom is acquired via 48 ways (Pirkei Avoth 6:6)
In other fields
Forty-eight is also:
- the number of hours in two days, and hence also part of the title of the movies 48 Hrs. and Another 48 Hrs.
- 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 car number of NASCAR Nextel Cup driver Jimmie Johnson
- 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.
- Historical years: AD 48, 48 BC, or 1948.
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