48768 has 32 divisors (see below), whose sum is σ = 130560. Its totient is φ = 16128.

The previous prime is 48767. The next prime is 48779. The reversal of 48768 is 86784.

It is a tau number, because it is divible by the number of its divisors (32).

It is not an unprimeable number, because it can be changed into a prime (48761) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 321 + ... + 447.

It is an arithmetic number, because the mean of its divisors is an integer number (4080).

2⁴⁸⁷⁶⁸ is an apocalyptic number.

48768 is a gapful number since it is divisible by the number (48) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 48768, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (65280).

48768 is an abundant number, since it is smaller than the sum of its proper divisors (81792).

It is a pseudoperfect number, because it is the sum of a subset of its proper divisors.

48768 is a wasteful number, since it uses less digits than its factorization.

48768 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 144 (or 132 counting only the distinct ones).

The product of its digits is 10752, while the sum is 33.

The square root of 48768 is about 220.8347798695. The cubic root of 48768 is about 36.5352134054.

It can be divided in two parts, 4876 and 8, that added together give a palindrome (4884).

The spelling of 48768 in words is "forty-eight thousand, seven hundred sixty-eight".