3968330400 has 576 divisors, whose sum is σ = 15490258560. Its totient is φ = 976896000.

The previous prime is 3968330393. The next prime is 3968330411. The reversal of 3968330400 is 40338693.

3968330400 is digitally balanced in base 2, because in such base it contains all the possibile digits an equal number of times.

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

It is an unprimeable number.

It is a polite number, since it can be written in 95 ways as a sum of consecutive naturals, for example, 37087147 + ... + 37087253.

It is an arithmetic number, because the mean of its divisors is an integer number (26892810).

Almost surely, 2^3968330400 is an apocalyptic number.

3968330400 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 3968330400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (7745129280).

3968330400 is an abundant number, since it is smaller than the sum of its proper divisors (11521928160).

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

3968330400 is a wasteful number, since it uses less digits than its factorization.

3968330400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 254 (or 235 counting only the distinct ones).

The product of its (nonzero) digits is 46656, while the sum is 36.

The square root of 3968330400 is about 62994.6854901269. The cubic root of 3968330400 is about 1583.2005837611.

The spelling of 3968330400 in words is "three billion, nine hundred sixty-eight million, three hundred thirty thousand, four hundred".