728964 has 18 divisors (see below), whose sum is σ = 1842750. Its totient is φ = 242976.

The previous prime is 728953. The next prime is 728969. The reversal of 728964 is 469827.

728964 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 only one way, i.e., 562500 + 166464 = 750^2 + 408^2 .

It is a tau number, because it is divible by the number of its divisors (18).

It is a Harshad number since it is a multiple of its sum of digits (36), and also a Moran number because the ratio is a prime number: 20249 = 728964 / (7 + 2 + 8 + 9 + 6 + 4).

It is not an unprimeable number, because it can be changed into a prime (728969) by changing a digit.

728964 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a polite number, since it can be written in 5 ways as a sum of consecutive naturals, for example, 10089 + ... + 10160.

It is an arithmetic number, because the mean of its divisors is an integer number (102375).

2⁷²⁸⁹⁶⁴ is an apocalyptic number.

It is an amenable number.

728964 is an abundant number, since it is smaller than the sum of its proper divisors (1113786).

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

728964 is a wasteful number, since it uses less digits than its factorization.

728964 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 20259 (or 20254 counting only the distinct ones).

The product of its digits is 24192, while the sum is 36.

The square root of 728964 is about 853.7938861341. The cubic root of 728964 is about 89.9985184941.

Adding to 728964 its sum of digits (36), we get a cube (729000 = 90³).

It can be divided in two parts, 72896 and 4, that added together give a square (72900 = 270²).

The spelling of 728964 in words is "seven hundred twenty-eight thousand, nine hundred sixty-four".