85952200550400 has 720 divisors, whose sum is σ = 322710710622300. Its totient is φ = 22606526545920.

The previous prime is 85952200550393. The next prime is 85952200550453. The reversal of 85952200550400 is 405500225958.

85952200550400 is a `hidden beast` number, since 8 + 5 + 9 + 52 + 2 + 0 + 0 + 550 + 40 + 0 = 666.

It can be written as a sum of positive squares in 6 ways, for example, as 19368167261184 + 66584033289216 = 4400928^2 + 8159904^2 .

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 an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (17) of ones.

It is a polite number, since it can be written in 59 ways as a sum of consecutive naturals, for example, 302603646 + ... + 302887554.

Almost surely, 2^{85952200550400} is an apocalyptic number.

85952200550400 is a gapful number since it is divisible by the number (80) 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 85952200550400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (161355355311150).

85952200550400 is an abundant number, since it is smaller than the sum of its proper divisors (236758510071900).

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

85952200550400 is a wasteful number, since it uses less digits than its factorization.

85952200550400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 284026 (or 283992 counting only the distinct ones).

The product of its (nonzero) digits is 720000, while the sum is 45.

The spelling of 85952200550400 in words is "eighty-five trillion, nine hundred fifty-two billion, two hundred million, five hundred fifty thousand, four hundred".