393768 has 32 divisors (see below), whose sum is σ = 1094400. Its totient is φ = 131184.

The previous prime is 393761. The next prime is 393779. The reversal of 393768 is 867393.

It is a Harshad number since it is a multiple of its sum of digits (36).

It is not an unprimeable number, because it can be changed into a prime (393761) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (5) of ones.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 696 + ... + 1127.

It is an arithmetic number, because the mean of its divisors is an integer number (34200).

2³⁹³⁷⁶⁸ is an apocalyptic number.

It is an amenable number.

393768 is an abundant number, since it is smaller than the sum of its proper divisors (700632).

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

393768 is a wasteful number, since it uses less digits than its factorization.

393768 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1838 (or 1828 counting only the distinct ones).

The product of its digits is 27216, while the sum is 36.

The square root of 393768 is about 627.5093624800. The cubic root of 393768 is about 73.2959773010.

It can be divided in two parts, 3937 and 68, that added together give a triangular number (4005 = T₈₉).

The spelling of 393768 in words is "three hundred ninety-three thousand, seven hundred sixty-eight".