85688064 has 432 divisors, whose sum is σ = 335543040. Its totient is φ = 21288960.

The previous prime is 85688063. The next prime is 85688077. The reversal of 85688064 is 46088658.

85688064 is a `hidden beast` number, since 8 + 568 + 80 + 6 + 4 = 666.

It is a tau number, because it is divible by the number of its divisors (432).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (85688063) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 3725557 + ... + 3725579.

It is an arithmetic number, because the mean of its divisors is an integer number (776720).

Almost surely, 2^85688064 is an apocalyptic number.

85688064 is a gapful number since it is divisible by the number (84) 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 85688064, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (167771520).

85688064 is an abundant number, since it is smaller than the sum of its proper divisors (249854976).

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

85688064 is a wasteful number, since it uses less digits than its factorization.

85688064 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 73 (or 46 counting only the distinct ones).

The product of its (nonzero) digits is 368640, while the sum is 45.

The square root of 85688064 is about 9256.7847549784. The cubic root of 85688064 is about 440.8661725443.

The spelling of 85688064 in words is "eighty-five million, six hundred eighty-eight thousand, sixty-four".