729075600 has 720 divisors, whose sum is σ = 3163458240. Its totient is φ = 157593600.

The previous prime is 729075593. The next prime is 729075647. The reversal of 729075600 is 6570927.

729075600 is a `hidden beast` number, since 7 + 2 + 90 + 7 + 560 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (720).

It is a Harshad number since it is a multiple of its sum of digits (36).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 143 ways as a sum of consecutive naturals, for example, 38372391 + ... + 38372409.

It is an arithmetic number, because the mean of its divisors is an integer number (4393692).

Almost surely, 2^729075600 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 729075600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1581729120).

729075600 is an abundant number, since it is smaller than the sum of its proper divisors (2434382640).

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

729075600 is a wasteful number, since it uses less digits than its factorization.

729075600 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 93 (or 57 counting only the distinct ones).

The product of its (nonzero) digits is 26460, while the sum is 36.

The square root of 729075600 is about 27001.3999637056. The cubic root of 729075600 is about 900.0311100357.

The spelling of 729075600 in words is "seven hundred twenty-nine million, seventy-five thousand, six hundred".