48 (number)

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