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48 (number)

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← 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
Senary1206
Octal608
Duodecimal4012
Hexadecimal3016

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, a highly composite number. Like all other multiples of 6, it is a semiperfect number. 48 is the second 17-gonal number.

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.

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

48 is in base 10 a Harshad number. 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

Astronomy

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 sports

In other fields

Forty-eight may also refer to:

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