85161585600 has 2016 divisors, whose sum is σ = 404469112320. Its totient is φ = 17139548160.

The previous prime is 85161585589. The next prime is 85161585653. The reversal of 85161585600 is 658516158.

85161585600 is a `hidden beast` number, since 8 + 5 + 1 + 6 + 1 + 585 + 60 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (2016).

It is a super-2 number, since 2×85161585600² (a number of 23 digits) contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (45).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 287 ways as a sum of consecutive naturals, for example, 1026043159 + ... + 1026043241.

It is an arithmetic number, because the mean of its divisors is an integer number (200629520).

Almost surely, 2^85161585600 is an apocalyptic number.

85161585600 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 85161585600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (202234556160).

85161585600 is an abundant number, since it is smaller than the sum of its proper divisors (319307526720).

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

85161585600 is a wasteful number, since it uses less digits than its factorization.

85161585600 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 169 (or 142 counting only the distinct ones).

The product of its (nonzero) digits is 288000, while the sum is 45.

It can be divided in two parts, 85161 and 585600, that added together give a square (670761 = 819²).

The spelling of 85161585600 in words is "eighty-five billion, one hundred sixty-one million, five hundred eighty-five thousand, six hundred".