199749572164800 has 1680 divisors, whose sum is σ = 846994220590848. Its totient is φ = 45230640537600.

The previous prime is 199749572164763. The next prime is 199749572164819. The reversal of 199749572164800 is 8461275947991.

199749572164800 is a `hidden beast` number, since 1 + 9 + 9 + 7 + 4 + 9 + 572 + 1 + 6 + 48 + 0 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (1680).

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

It is an unprimeable number.

It is a polite number, since it can be written in 239 ways as a sum of consecutive naturals, for example, 43452156102 + ... + 43452160698.

Almost surely, 2^{199749572164800} is an apocalyptic number.

199749572164800 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 199749572164800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (423497110295424).

199749572164800 is an abundant number, since it is smaller than the sum of its proper divisors (647244648426048).

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

199749572164800 is a wasteful number, since it uses less digits than its factorization.

199749572164800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 5076 (or 5052 counting only the distinct ones).

The product of its (nonzero) digits is 274337280, while the sum is 72.

The spelling of 199749572164800 in words is "one hundred ninety-nine trillion, seven hundred forty-nine billion, five hundred seventy-two million, one hundred sixty-four thousand, eight hundred".