728208000 has 384 divisors, whose sum is σ = 2823584400. Its totient is φ = 178790400.

The previous prime is 728207999. The next prime is 728208023. The reversal of 728208000 is 802827.

It can be written as a sum of positive squares in 8 ways, for example, as 17239104 + 710968896 = 4152^2 + 26664^2 .

It is a tau number, because it is divible by the number of its divisors (384).

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 1871806 + ... + 1872194.

Almost surely, 2^728208000 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 728208000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1411792200).

728208000 is an abundant number, since it is smaller than the sum of its proper divisors (2095376400).

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

728208000 is a wasteful number, since it uses less digits than its factorization.

728208000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 437 (or 412 counting only the distinct ones).

The product of its (nonzero) digits is 1792, while the sum is 27.

The square root of 728208000 is about 26985.3293476289. The cubic root of 728208000 is about 899.6739559720.

The spelling of 728208000 in words is "seven hundred twenty-eight million, two hundred eight thousand".