48 (number)
48 (forty-eight) is the natural number following 47 and preceding 49. It is one third of a gross, or four dozens.
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| 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 | |||
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
- The atomic number of cadmium
- The number of Ptolemaic constellations
- The number of symmetries of a cube
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
In religion
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:
- the code for international direct dial phone calls to Poland
- the model number of the HP-48 S/SX/G/GX/G+/GII
- the 48 Hour Film Project
- The First 48, an American crime program, 2004-present
- 48 Hours is a television news program on CBS
- 48 Hrs., a 1982 film starring Nick Nolte and Eddie Murphy, followed by Another 48 Hrs.
- Arizona is the 48th state in the Union
- The 48 United States (excluding Alaska and Hawaii) are also referred to as the "Lower 48" or the "48 contiguous states"
- '48 is an alternate history novel by James Herbert
- The 48 Laws of Power is a book by Robert Greene
- The number 48 in ASCII is what you add to any single digit integer to convert to its ASCII value
- MAC address uses 48-bit (6-byte)
- The number of the French department Lozère
- a model of Harley-Davidson in the Sportster line.
- In Chinese Numerology, 48 is an auspicious number meaning 'determined to prosper', or simply 'prosperity'; which is good for business.
- 48 is the number Mountain peaks in New Hampshire over 4000 feet above sea level, as defined by the Appalachian Mountain Club.
References
- "Sloane's A000165 : Double factorials". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
- "Sloane's A002182 : Highly composite numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
- "Sloane's A005835 : Pseudoperfect (or semiperfect) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
- "Sloane's A051869 : 17-gonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
- "Sloane's A097942 : Highly totient numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
- "Sloane's A005528 : Størmer numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
- "Sloane's A005349 : Niven (or Harshad) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
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