393216000 has 168 divisors, whose sum is σ = 1308622224. Its totient is φ = 104857600.

The previous prime is 393215989. The next prime is 393216007. The reversal of 393216000 is 612393.

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

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (393216007) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 78643198 + ... + 78643202.

It is an arithmetic number, because the mean of its divisors is an integer number (7789418).

Almost surely, 2^393216000 is an apocalyptic number.

393216000 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 393216000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (654311112).

393216000 is an abundant number, since it is smaller than the sum of its proper divisors (915406224).

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

393216000 is an frugal number, since it uses more digits than its factorization.

393216000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 58 (or 10 counting only the distinct ones).

The product of its (nonzero) digits is 972, while the sum is 24.

The square root of 393216000 is about 19829.6747325820. The cubic root of 393216000 is about 732.6171152341.

Adding to 393216000 its reverse (612393), we get a palindrome (393828393).

The spelling of 393216000 in words is "three hundred ninety-three million, two hundred sixteen thousand".