# 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 →
Cardinalforty-eight
Ordinal48th
(forty-eighth)
Factorization24 × 3
Divisors1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Greek numeralΜΗ´
Roman numeralXLVIII
Binary1100002
Ternary12103
Quaternary3004
Quinary1435
Senary1206
Octal608
Duodecimal4012
Vigesimal2820
Base 361C36

## 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 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 idol girl band

## In sports

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

## In other fields

Forty-eight may also refer to:

## 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.
8. ^ [1]