393940800 has 336 divisors, whose sum is σ = 1568500800. Its totient is φ = 95385600.

The previous prime is 393940787. The next prime is 393940801. The reversal of 393940800 is 8049393.

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

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (393940801) by changing a digit.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 474786 + ... + 475614.

Almost surely, 2^393940800 is an apocalyptic number.

393940800 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 393940800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (784250400).

393940800 is an abundant number, since it is smaller than the sum of its proper divisors (1174560000).

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

393940800 is a wasteful number, since it uses less digits than its factorization.

393940800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 871 (or 850 counting only the distinct ones).

The product of its (nonzero) digits is 23328, while the sum is 36.

The square root of 393940800 is about 19847.9419588027. The cubic root of 393940800 is about 733.0669739725.

The spelling of 393940800 in words is "three hundred ninety-three million, nine hundred forty thousand, eight hundred".