48960 has 84 divisors (see below), whose sum is σ = 178308. Its totient is φ = 12288.

The previous prime is 48953. The next prime is 48973. The reversal of 48960 is 6984.

48960 is digitally balanced in base 2, because in such base it contains all the possibile digits an equal number of times.

It can be written as a sum of positive squares in 2 ways, for example, as 28224 + 20736 = 168^2 + 144^2 .

It is a congruent number.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 48960.

It is an unprimeable number.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 2872 + ... + 2888.

2⁴⁸⁹⁶⁰ is an apocalyptic number.

48960 is a gapful number since it is divisible by the number (40) 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 48960, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (89154).

48960 is an abundant number, since it is smaller than the sum of its proper divisors (129348).

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

48960 is a wasteful number, since it uses less digits than its factorization.

48960 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 40 (or 27 counting only the distinct ones).

The product of its (nonzero) digits is 1728, while the sum is 27.

The square root of 48960 is about 221.2690669750. The cubic root of 48960 is about 36.5830970951.

The spelling of 48960 in words is "forty-eight thousand, nine hundred sixty".