729320400 has 270 divisors, whose sum is σ = 2692416402. Its totient is φ = 182784000.

The previous prime is 729320387. The next prime is 729320401. The reversal of 729320400 is 4023927.

729320400 is digitally balanced in base 2, because in such base it contains all the possibile digits an equal number of times.

It can be written as a sum of positive squares in 9 ways, for example, as 968256 + 728352144 = 984^2 + 26988^2 .

It is a super-3 number, since 3×729320400³ (a number of 28 digits) contains 333 as substring.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (729320401) by changing a digit.

It is a polite number, since it can be written in 53 ways as a sum of consecutive naturals, for example, 1040050 + ... + 1040750.

Almost surely, 2^729320400 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 729320400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1346208201).

729320400 is an abundant number, since it is smaller than the sum of its proper divisors (1963096002).

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

729320400 is a wasteful number, since it uses less digits than its factorization.

729320400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 759 (or 728 counting only the distinct ones).

The product of its (nonzero) digits is 3024, while the sum is 27.

The square root of 729320400 is about 27005.9326815424. The cubic root of 729320400 is about 900.1318325400.

The spelling of 729320400 in words is "seven hundred twenty-nine million, three hundred twenty thousand, four hundred".