393264 has 30 divisors (see below), whose sum is σ = 1100996. Its totient is φ = 131040.

The previous prime is 393257. The next prime is 393271. The reversal of 393264 is 462393.

393264 = T₁₅₇ + T₁₅₈ + ... + T₁₈₃.

393264 is digitally balanced in base 3, because in such base it contains all the possibile digits an equal number of times.

It is an interprime number because it is at equal distance from previous prime (393257) and next prime (393271).

It is a Smith number, since the sum of its digits (27) coincides with the sum of the digits of its prime factors.

It is a nude number because it is divisible by every one of its digits.

It is a zygodrome in base 2.

It is an unprimeable number.

393264 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, 1222 + ... + 1509.

2³⁹³²⁶⁴ is an apocalyptic number.

It is an amenable number.

393264 is an abundant number, since it is smaller than the sum of its proper divisors (707732).

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

393264 is a wasteful number, since it uses less digits than its factorization.

393264 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 2745 (or 2736 counting only the distinct ones).

The product of its digits is 3888, while the sum is 27.

The square root of 393264 is about 627.1076462618. The cubic root of 393264 is about 73.2646924288.

Subtracting from 393264 its product of digits (3888), we obtain a square (389376 = 624²).

The spelling of 393264 in words is "three hundred ninety-three thousand, two hundred sixty-four".