728768640 has 128 divisors (see below), whose sum is σ = 2344204800. Its totient is φ = 192561152.

The previous prime is 728768633. The next prime is 728768641. The reversal of 728768640 is 46867827.

It is a tau number, because it is divible by the number of its divisors (128).

It is a super-2 number, since 2×728768640² = 1062207461294899200, which contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (48).

It is a self number, because there is not a number n which added to its sum of digits gives 728768640.

It is not an unprimeable number, because it can be changed into a prime (728768641) by changing a digit.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 215281 + ... + 218639.

It is an arithmetic number, because the mean of its divisors is an integer number (18314100).

Almost surely, 2^728768640 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 728768640, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1172102400).

728768640 is an abundant number, since it is smaller than the sum of its proper divisors (1615436160).

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

728768640 is a wasteful number, since it uses less digits than its factorization.

728768640 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 3494 (or 3482 counting only the distinct ones).

The product of its (nonzero) digits is 903168, while the sum is 48.

The square root of 728768640 is about 26995.7152155671. The cubic root of 728768640 is about 899.9047800495.

The spelling of 728768640 in words is "seven hundred twenty-eight million, seven hundred sixty-eight thousand, six hundred forty".