• 48 can be written using four 4's:
48 has 10 divisors (see below), whose sum is σ = 124. Its totient is φ = 16.
The previous prime is 47. The next prime is 53. The reversal of 48 is 84.
It is a Jordan-Polya number, since it can be written as 4! ⋅ 2!.
It is a double factorial (48 = 6 !! = 2 ⋅ 4 ⋅ 6 ).
48 is nontrivially palindromic in base 7, base 11 and base 15.
It is a Cunningham number, because it is equal to 72-1.
48 is an esthetic number in base 3, because in such base its adjacent digits differ by 1.
Together with 75 it forms a betrothed pair.
It is a Harshad number since it is a multiple of its sum of digits (12).
It is a super Niven number, because it is divisible the sum of any subset of its (nonzero) digits.
It is a nude number because it is divisible by every one of its digits.
48 is an idoneal number.
It is an Ulam number.
It is one of the 548 Lynch-Bell numbers.
48 is a nontrivial repdigit in base 7, base 11 and base 15.
It is a plaindrome in base 7, base 10, base 11, base 13, base 14 and base 15.
It is a nialpdrome in base 2, base 4, base 7, base 8, base 9, base 11, base 12, base 15 and base 16.
It is a zygodrome in base 2, base 7, base 11 and base 15.
It is a pernicious number, because its binary representation contains a prime number (2) of ones.
A polygon with 48 sides can be constructed with ruler and compass.
It is a polite number, since it can be written as a sum of consecutive naturals, namely, 15 + 16 + 17.
48 is a highly composite number, because it has more divisors than any smaller number.
48 is a superabundant number, because it has a larger abundancy index than any smaller number.
It is an amenable number.
It is a practical number, because each smaller number is the sum of distinct divisors of 48, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (62).
48 is an abundant number, since it is smaller than the sum of its proper divisors (76).
It is a pseudoperfect number, because it is the sum of a subset of its proper divisors.
48 is a wasteful number, since it uses less digits than its factorization.
48 is an evil number, because the sum of its binary digits is even.
The sum of its prime factors is 11 (or 5 counting only the distinct ones).
The product of its digits is 32, while the sum is 12.
The square root of 48 is about 6.9282032303. The cubic root of 48 is about 3.6342411857.
Subtracting from 48 its sum of digits (12), we obtain a triangular number (36 = T8).
Multiplying 48 by its sum of digits (12), we get a square (576 = 242).
Subtracting from 48 its product of digits (32), we obtain a 4-th power (16 = 24).
Subtracting 48 from its reverse (84), we obtain a triangular number (36 = T8).
The spelling of 48 in words is "forty-eight", and thus it is an aban number and an uban number.
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