393120 has 192 divisors, whose sum is σ = 1693440. Its totient is φ = 82944.

The previous prime is 393109. The next prime is 393121. The reversal of 393120 is 21393.

It is a Harshad number since it is a multiple of its sum of digits (18).

It is a zygodrome in base 4.

It is a junction number, because it is equal to n+sod(n) for n = 393093 and 393102.

It is a congruent number.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 393120.

It is not an unprimeable number, because it can be changed into a prime (393121) by changing a digit.

It is a polite number, since it can be written in 31 ways as a sum of consecutive naturals, for example, 30234 + ... + 30246.

It is an arithmetic number, because the mean of its divisors is an integer number (8820).

2³⁹³¹²⁰ is an apocalyptic number.

393120 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 393120, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (846720).

393120 is an abundant number, since it is smaller than the sum of its proper divisors (1300320).

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

393120 is a wasteful number, since it uses less digits than its factorization.

393120 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 44 (or 30 counting only the distinct ones).

The product of its (nonzero) digits is 162, while the sum is 18.

The square root of 393120 is about 626.9928229254. The cubic root of 393120 is about 73.2557489848.

The spelling of 393120 in words is "three hundred ninety-three thousand, one hundred twenty".