48 is the smallest number with exactly ten divisors, and the first multiple of 12 not to be a sum of
twin primes.
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
Buddhism,
Amitabha Buddha had made 48 great vows and promises to provide ultimate salvation to countless beings through countless eons, with benefits said to be available merely by thinking about his name with
Nianfo practice. He is thus hailed as "King of Buddhas" through such skillful compassion and became a popular and formal refuge figure in
Pureland Buddhism.
In music
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.