85668610464 has 288 divisors, whose sum is σ = 260829026640. Its totient is φ = 26621952000.

The previous prime is 85668610451. The next prime is 85668610483. The reversal of 85668610464 is 46401686658.

85668610464 is a `hidden beast` number, since 8 + 566 + 8 + 6 + 10 + 4 + 64 = 666.

It can be written as a sum of positive squares in 8 ways, for example, as 44905000464 + 40763610000 = 211908^2 + 201900^2 .

It is a tau number, because it is divible by the number of its divisors (288).

It is a super-4 number, since 4×85668610464⁴ (a number of 45 digits) contains 4444 as substring. Note that it is a super-d number also for d = 2.

It is a Smith number, since the sum of its digits (54) coincides with the sum of the digits of its prime factors.

It is a self number, because there is not a number n which added to its sum of digits gives 85668610464.

It is an unprimeable number.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 34584394 + ... + 34586870.

Almost surely, 2^85668610464 is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 85668610464, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (130414513320).

85668610464 is an abundant number, since it is smaller than the sum of its proper divisors (175160416176).

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

85668610464 is a wasteful number, since it uses less digits than its factorization.

85668610464 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 2664 (or 2653 counting only the distinct ones).

The product of its (nonzero) digits is 6635520, while the sum is 54.

The spelling of 85668610464 in words is "eighty-five billion, six hundred sixty-eight million, six hundred ten thousand, four hundred sixty-four".