3968546400 has 720 divisors, whose sum is σ = 17838795744. Its totient is φ = 836075520.

The previous prime is 3968546389. The next prime is 3968546459. The reversal of 3968546400 is 46458693.

3968546400 is a `hidden beast` number, since 3 + 9 + 68 + 546 + 40 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (720).

It is a Harshad number since it is a multiple of its sum of digits (45).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 119 ways as a sum of consecutive naturals, for example, 5896464 + ... + 5897136.

Almost surely, 2^3968546400 is an apocalyptic number.

3968546400 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 3968546400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (8919397872).

3968546400 is an abundant number, since it is smaller than the sum of its proper divisors (13870249344).

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

3968546400 is a wasteful number, since it uses less digits than its factorization.

3968546400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 725 (or 703 counting only the distinct ones).

The product of its (nonzero) digits is 622080, while the sum is 45.

The square root of 3968546400 is about 62996.3998971370. The cubic root of 3968546400 is about 1583.2293082780.

The spelling of 3968546400 in words is "three billion, nine hundred sixty-eight million, five hundred forty-six thousand, four hundred".