393360 has 80 divisors (see below), whose sum is σ = 1339200. Its totient is φ = 94720.

The previous prime is 393331. The next prime is 393361. The reversal of 393360 is 63393.

It is a tau number, because it is divible by the number of its divisors (80).

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

It is a self number, because there is not a number n which added to its sum of digits gives 393360.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 393360.

It is not an unprimeable number, because it can be changed into a prime (393361) by changing a digit.

393360 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 15 ways as a sum of consecutive naturals, for example, 2566 + ... + 2714.

It is an arithmetic number, because the mean of its divisors is an integer number (16740).

2³⁹³³⁶⁰ is an apocalyptic number.

393360 is a gapful number since it is divisible by the number (30) 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 393360, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (669600).

393360 is an abundant number, since it is smaller than the sum of its proper divisors (945840).

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

393360 is a wasteful number, since it uses less digits than its factorization.

393360 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 176 (or 170 counting only the distinct ones).

The product of its (nonzero) digits is 1458, while the sum is 24.

The square root of 393360 is about 627.1841834740. The cubic root of 393360 is about 73.2706535120.

It can be divided in two parts, 3933 and 60, that added together give a palindrome (3993).

The spelling of 393360 in words is "three hundred ninety-three thousand, three hundred sixty".