85384396800 has 576 divisors, whose sum is σ = 315131338860. Its totient is φ = 22083010560.

The previous prime is 85384396789. The next prime is 85384396813. The reversal of 85384396800 is 869348358.

It is a happy number.

85384396800 is a `hidden beast` number, since 8 + 538 + 43 + 9 + 68 + 0 + 0 = 666.

It can be written as a sum of positive squares in 6 ways, for example, as 20957773824 + 64426622976 = 144768^2 + 253824^2 .

It is a tau number, because it is divible by the number of its divisors (576).

It is an unprimeable number.

It is a polite number, since it can be written in 35 ways as a sum of consecutive naturals, for example, 272793444 + ... + 272793756.

Almost surely, 2^85384396800 is an apocalyptic number.

85384396800 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 85384396800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (157565669430).

85384396800 is an abundant number, since it is smaller than the sum of its proper divisors (229746942060).

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

85384396800 is a wasteful number, since it uses less digits than its factorization.

85384396800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 396 (or 360 counting only the distinct ones).

The product of its (nonzero) digits is 4976640, while the sum is 54.

The spelling of 85384396800 in words is "eighty-five billion, three hundred eighty-four million, three hundred ninety-six thousand, eight hundred".