# 48 (number)

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

| ||||
---|---|---|---|---|

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 | 110000_{2} | |||

Ternary | 1210_{3} | |||

Quaternary | 300_{4} | |||

Quinary | 143_{5} | |||

Senary | 120_{6} | |||

Octal | 60_{8} | |||

Duodecimal | 40_{12} | |||

Hexadecimal | 30_{16} | |||

Vigesimal | 28_{20} | |||

Base 36 | 1C_{36} |

## In mathematicsEdit

**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 48^{2} + 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 scienceEdit

- The atomic number of cadmium
- The number of Ptolemaic constellations
- The number of symmetries of a cube

## AstronomyEdit

- 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 religionEdit

- 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 musicEdit

- 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 idol girl band

## In sportsEdit

- 48 is the total number of minutes in a full NBA game.

## In other fieldsEdit

**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.
^{[citation needed]} - 48 is the number Mountain peaks in New Hampshire over 4000 feet above sea level, as defined by the Appalachian Mountain Club.

## ReferencesEdit

**^**"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.**^**[1]