72048000 has 256 divisors, whose sum is σ = 254592000. Its totient is φ = 17971200.

The previous prime is 72047993. The next prime is 72048001. The reversal of 72048000 is 84027.

It is a happy number.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (72048001) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 31 ways as a sum of consecutive naturals, for example, 911961 + ... + 912039.

It is an arithmetic number, because the mean of its divisors is an integer number (994500).

Almost surely, 2^72048000 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 72048000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (127296000).

72048000 is an abundant number, since it is smaller than the sum of its proper divisors (182544000).

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

72048000 is a wasteful number, since it uses less digits than its factorization.

72048000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 130 (or 108 counting only the distinct ones).

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

The square root of 72048000 is about 8488.1093301159. The cubic root of 72048000 is about 416.1091922439.

The spelling of 72048000 in words is "seventy-two million, forty-eight thousand".