729312 has 48 divisors (see below), whose sum is σ = 1959552. Its totient is φ = 237440.

The previous prime is 729301. The next prime is 729329. The reversal of 729312 is 213927.

It is a tau number, because it is divible by the number of its divisors (48).

It is a Harshad number since it is a multiple of its sum of digits (24).

It is a congruent number.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 729312.

It is an unprimeable number.

729312 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 6763 + ... + 6869.

It is an arithmetic number, because the mean of its divisors is an integer number (40824).

2⁷²⁹³¹² 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 729312, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (979776).

729312 is an abundant number, since it is smaller than the sum of its proper divisors (1230240).

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

729312 is a wasteful number, since it uses less digits than its factorization.

729312 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 191 (or 183 counting only the distinct ones).

The product of its digits is 756, while the sum is 24.

The square root of 729312 is about 853.9976580764. The cubic root of 729312 is about 90.0128376749.

The spelling of 729312 in words is "seven hundred twenty-nine thousand, three hundred twelve".