48 (number)

(Redirected from Forty-eight)
 ← 47 48 49 →
Cardinal forty-eight
Ordinal 48th
(forty-eighth)
Factorization 24× 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
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 a Harshad number in base 10.[7] It has 24, 2, 12, and 4 as factors.

In religion

• The prophecies of 48 Jewish prophets and 7 prophetesses [1] 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 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.