393408 has 42 divisors (see below), whose sum is σ = 1129284. Its totient is φ = 130944.

The previous prime is 393403. The next prime is 393413. The reversal of 393408 is 804393.

It is an interprime number because it is at equal distance from previous prime (393403) and next prime (393413).

It is a zygodrome in base 2.

It is not an unprimeable number, because it can be changed into a prime (393401) by changing a digit.

393408 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, 235 + ... + 917.

2³⁹³⁴⁰⁸ 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 393408, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (564642).

393408 is an abundant number, since it is smaller than the sum of its proper divisors (735876).

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

393408 is a wasteful number, since it uses less digits than its factorization.

393408 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 701 (or 688 counting only the distinct ones).

The product of its (nonzero) digits is 2592, while the sum is 27.

The square root of 393408 is about 627.2224485779. Note that the first 3 decimals coincide. The cubic root of 393408 is about 73.2736336899.

The spelling of 393408 in words is "three hundred ninety-three thousand, four hundred eight".