85968000 has 256 divisors, whose sum is σ = 318240000. Its totient is φ = 22809600.

The previous prime is 85967969. The next prime is 85968011. The reversal of 85968000 is 86958.

It is a Harshad number since it is a multiple of its sum of digits (36).

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 31 ways as a sum of consecutive naturals, for example, 431901 + ... + 432099.

It is an arithmetic number, because the mean of its divisors is an integer number (1243125).

Almost surely, 2^85968000 is an apocalyptic number.

85968000 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 85968000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (159120000).

85968000 is an abundant number, since it is smaller than the sum of its proper divisors (232272000).

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

85968000 is a wasteful number, since it uses less digits than its factorization.

85968000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 237 (or 209 counting only the distinct ones).

The product of its (nonzero) digits is 17280, while the sum is 36.

The square root of 85968000 is about 9271.8930105993. The cubic root of 85968000 is about 441.3457421041.

The spelling of 85968000 in words is "eighty-five million, nine hundred sixty-eight thousand".