48072 has 16 divisors (see below), whose sum is σ = 120240. Its totient is φ = 16016.

The previous prime is 48049. The next prime is 48073. The reversal of 48072 is 27084.

It is a happy number.

It is a super-3 number, since 3×48072³ = 333271232607744, which contains 333 as substring.

48072 is a modest number, since divided by 72 gives 48 as remainder.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 48072.

It is not an unprimeable number, because it can be changed into a prime (48073) by changing a digit.

48072 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 978 + ... + 1025.

It is an arithmetic number, because the mean of its divisors is an integer number (7515).

2⁴⁸⁰⁷² is an apocalyptic number.

It is an amenable number.

48072 is an abundant number, since it is smaller than the sum of its proper divisors (72168).

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

It is a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (60120).

48072 is a wasteful number, since it uses less digits than its factorization.

48072 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 2012 (or 2008 counting only the distinct ones).

The product of its (nonzero) digits is 448, while the sum is 21.

The square root of 48072 is about 219.2532781967. The cubic root of 48072 is about 36.3605739845.

The spelling of 48072 in words is "forty-eight thousand, seventy-two".