72048 has 40 divisors (see below), whose sum is σ = 198400. Its totient is φ = 22464.

The previous prime is 72047. The next prime is 72053. The reversal of 72048 is 84027.

It is a happy number.

72048 is nontrivially palindromic in base 7.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (72043) 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 7 ways as a sum of consecutive naturals, for example, 873 + ... + 951.

It is an arithmetic number, because the mean of its divisors is an integer number (4960).

2⁷²⁰⁴⁸ is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 72048, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (99200).

72048 is an abundant number, since it is smaller than the sum of its proper divisors (126352).

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

72048 is a wasteful number, since it uses less digits than its factorization.

72048 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 109 (or 103 counting only the distinct ones).

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

The square root of 72048 is about 268.4175851169. The cubic root of 72048 is about 41.6109192244.

Subtracting from 72048 its sum of digits (21), we obtain a palindrome (72027).

The spelling of 72048 in words is "seventy-two thousand, forty-eight".