728352000 has 360 divisors, whose sum is σ = 2720069352. Its totient is φ = 193536000.

The previous prime is 728351989. The next prime is 728352007. The reversal of 728352000 is 253827.

It can be written as a sum of positive squares in 4 ways, for example, as 10969344 + 717382656 = 3312^2 + 26784^2 .

It is a tau number, because it is divible by the number of its divisors (360).

It is a Harshad number since it is a multiple of its sum of digits (27).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (728352007) by changing a digit.

It is a polite number, since it can be written in 39 ways as a sum of consecutive naturals, for example, 2591860 + ... + 2592140.

Almost surely, 2^728352000 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 728352000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1360034676).

728352000 is an abundant number, since it is smaller than the sum of its proper divisors (1991717352).

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

728352000 is an equidigital number, since it uses as much as digits as its factorization.

728352000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 324 (or 291 counting only the distinct ones).

The product of its (nonzero) digits is 3360, while the sum is 27.

The square root of 728352000 is about 26987.9973321475. The cubic root of 728352000 is about 899.7332542819.

The spelling of 728352000 in words is "seven hundred twenty-eight million, three hundred fifty-two thousand".