85046385715200 has 5040 divisors, whose sum is σ = 402632313124860. Its totient is φ = 17698046607360.

The previous prime is 85046385715189. The next prime is 85046385715231. The reversal of 85046385715200 is 251758364058.

85046385715200 is a `hidden beast` number, since 8 + 5 + 0 + 4 + 63 + 8 + 57 + 1 + 520 + 0 = 666.

It can be written as a sum of positive squares in 6 ways, for example, as 18283628676096 + 66762757039104 = 4275936^2 + 8170848^2 .

It is a tau number, because it is divible by the number of its divisors (5040).

It is a super-3 number, since 3×85046385715200³ (a number of 43 digits) contains 333 as substring. Note that it is a super-d number also for d = 2.

It is a Harshad number since it is a multiple of its sum of digits (54).

It is an unprimeable number.

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 419 ways as a sum of consecutive naturals, for example, 1165018982364 + ... + 1165018982436.

Almost surely, 2^{85046385715200} is an apocalyptic number.

85046385715200 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 85046385715200, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (201316156562430).

85046385715200 is an abundant number, since it is smaller than the sum of its proper divisors (317585927409660).

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

85046385715200 is an frugal number, since it uses more digits than its factorization.

85046385715200 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 164 (or 103 counting only the distinct ones).

The product of its (nonzero) digits is 8064000, while the sum is 54.

The spelling of 85046385715200 in words is "eighty-five trillion, forty-six billion, three hundred eighty-five million, seven hundred fifteen thousand, two hundred".