393312 has 48 divisors (see below), whose sum is σ = 1097712. Its totient is φ = 122880.

The previous prime is 393311. The next prime is 393331. The reversal of 393312 is 213393.

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

It is a zygodrome in base 2.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (393311) by changing a digit.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 1512 + ... + 1752.

It is an arithmetic number, because the mean of its divisors is an integer number (22869).

2³⁹³³¹² is an apocalyptic number.

393312 is a gapful number since it is divisible by the number (32) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 393312, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (548856).

393312 is an abundant number, since it is smaller than the sum of its proper divisors (704400).

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

393312 is a wasteful number, since it uses less digits than its factorization.

393312 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 271 (or 263 counting only the distinct ones).

The product of its digits is 486, while the sum is 21.

The square root of 393312 is about 627.1459160355. The cubic root of 393312 is about 73.2676730916.

It can be divided in two parts, 3 and 93312, that multiplied together give a 7-th power (279936 = 6⁷).

The spelling of 393312 in words is "three hundred ninety-three thousand, three hundred twelve".