48 (number)

← 47 48 49 →
← 40 41 42 43 44 45 46 47 48 49 → List of numbers — Integers ← 0 10 20 30 40 50 60 70 80 90 →
Cardinal	forty-eight
Ordinal	48th (forty-eighth)
Factorization	2^4× 3
Divisors	1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Roman numeral	XLVIII
Binary	1100002
Ternary	12103
Quaternary	3004
Quinary	1435
Senary	1206
Octal	608
Duodecimal	4012
Hexadecimal	3016
Vigesimal	2820
Base 36	1C36

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

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.