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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Cardinal	forty-eight
Ordinal	48th (forty-eighth)
Factorization	2^4 × 3
Divisors	1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Greek numeral	ΜΗ´
Roman numeral	XLVIII
Binary	1100002
Ternary	12103
Octal	608
Duodecimal	4012
Hexadecimal	3016

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

• 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 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 United States.
• 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

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.