# 48 (number): Map

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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 a 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 the first number of the form (24.q) and 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.

## In religion

• The prophecies of 48 Jewish prophets and 7 prophetesses [48231] 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 other fields

Forty-eight may also refer to:

## Historical years

48 A.D., 48 B.C., 1848, 1948, 2048, etc.

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