48 (number)

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

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 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.^[5]

Since the greatest prime factor of 48² + 1 = 2305 is 461, which is clearly more than 48 twice, 48 is a Størmer number.^[6]

48 is in base 10 a Harshad number.^[7] It has 24, 2, 12, and 4 as factors.

48 is a Narcissistic number (but subtracted instead of added) as: |4² − 8²| = 48

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. 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 were recorded in the Tanakh for posterity
• According to the Mishnah, Torah wisdom is acquired via 48 ways (Pirkei Avoth 6:6)
• Siddhartha Gautama, the founder of Buddhism, sat under a bodhi tree for 48 days attempting to understand the nature of reality and Universe. Buddhism was the result.

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
• 48 Crash is a song by Suzi Quatro
• 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, by the thoughts of many peoples, it consists of approximately 48 members. In fact, the idol group consists more than 48 members.
• 48 is a song by Tyler, The Creator
• Forty eight is a song by Truckfighters off their 2007 album Phi

In sports

• 48 is the number of a NASCAR car owned by Hendrick Motorsports. It is currently being driven by six-time Sprint Cup Series champion Jimmie Johnson.
• 48 is the retired number of former U.S. President Gerald Ford's jersey at the University of Michigan.
• 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.

References