393948000 has 288 divisors, whose sum is σ = 1447310592. Its totient is φ = 101376000.

The previous prime is 393947989. The next prime is 393948001. The reversal of 393948000 is 849393.

It is a tau number, because it is divible by the number of its divisors (288).

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 (393948001) 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, 1115824 + ... + 1116176.

It is an arithmetic number, because the mean of its divisors is an integer number (5025384).

Almost surely, 2^393948000 is an apocalyptic number.

393948000 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 393948000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (723655296).

393948000 is an abundant number, since it is smaller than the sum of its proper divisors (1053362592).

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

393948000 is a wasteful number, since it uses less digits than its factorization.

393948000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 415 (or 394 counting only the distinct ones).

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

The square root of 393948000 is about 19848.1233369808. The cubic root of 393948000 is about 733.0714399989.

The spelling of 393948000 in words is "three hundred ninety-three million, nine hundred forty-eight thousand".