199975311712800 has 1728 divisors, whose sum is σ = 813124320712704. Its totient is φ = 47639284531200.

The previous prime is 199975311712739. The next prime is 199975311712801. The reversal of 199975311712800 is 8217113579991.

199975311712800 is a `hidden beast` number, since 1 + 9 + 9 + 9 + 7 + 531 + 1 + 7 + 12 + 80 + 0 = 666.

It is not an unprimeable number, because it can be changed into a prime (199975311712801) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (19) of ones.

It is a polite number, since it can be written in 287 ways as a sum of consecutive naturals, for example, 17859716802 + ... + 17859727998.

It is an arithmetic number, because the mean of its divisors is an integer number (470558055968).

Almost surely, 2^{199975311712800} is an apocalyptic number.

199975311712800 is a gapful number since it is divisible by the number (10) 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 199975311712800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (406562160356352).

199975311712800 is an abundant number, since it is smaller than the sum of its proper divisors (613149008999904).

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

199975311712800 is a wasteful number, since it uses less digits than its factorization.

199975311712800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 11473 (or 11448 counting only the distinct ones).

The product of its (nonzero) digits is 8573040, while the sum is 63.

The spelling of 199975311712800 in words is "one hundred ninety-nine trillion, nine hundred seventy-five billion, three hundred eleven million, seven hundred twelve thousand, eight hundred".