85968800 has 72 divisors (see below), whose sum is σ = 215072172. Its totient is φ = 33536000.

The previous prime is 85968793. The next prime is 85968823. The reversal of 85968800 is 886958.

It can be written as a sum of positive squares in 6 ways, for example, as 22543504 + 63425296 = 4748^2 + 7964^2 .

It is an unprimeable number.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 31490 + ... + 34110.

Almost surely, 2^85968800 is an apocalyptic number.

85968800 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 85968800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (107536086).

85968800 is an abundant number, since it is smaller than the sum of its proper divisors (129103372).

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

85968800 is a wasteful number, since it uses less digits than its factorization.

85968800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 2682 (or 2669 counting only the distinct ones).

The product of its (nonzero) digits is 138240, while the sum is 44.

The square root of 85968800 is about 9271.9361516352. The cubic root of 85968800 is about 441.3471111232.

It can be divided in two parts, 85968 and 800, that added together give a palindrome (86768).

The spelling of 85968800 in words is "eighty-five million, nine hundred sixty-eight thousand, eight hundred".