3998478556800 has 2880 divisors, whose sum is σ = 18834968469240. Its totient is φ = 827714764800.

The previous prime is 3998478556727. The next prime is 3998478556811. The reversal of 3998478556800 is 86558748993.

3998478556800 is a `hidden beast` number, since 3 + 9 + 98 + 478 + 5 + 5 + 68 + 0 + 0 = 666.

It can be written as a sum of positive squares in 12 ways, for example, as 101139264576 + 3897339292224 = 318024^2 + 1974168^2 .

It is a tau number, because it is divible by the number of its divisors (2880).

It is a Harshad number since it is a multiple of its sum of digits (72).

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (23) of ones.

It is a polite number, since it can be written in 359 ways as a sum of consecutive naturals, for example, 10071734202 + ... + 10071734598.

Almost surely, 2^{3998478556800} is an apocalyptic number.

3998478556800 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 3998478556800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (9417484234620).

3998478556800 is an abundant number, since it is smaller than the sum of its proper divisors (14836489912440).

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

3998478556800 is a wasteful number, since it uses less digits than its factorization.

3998478556800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 521 (or 488 counting only the distinct ones).

The product of its (nonzero) digits is 522547200, while the sum is 72.

The spelling of 3998478556800 in words is "three trillion, nine hundred ninety-eight billion, four hundred seventy-eight million, five hundred fifty-six thousand, eight hundred".