85648800 has 144 divisors (see below), whose sum is σ = 281981952. Its totient is φ = 22579200.

The previous prime is 85648781. The next prime is 85648807. The reversal of 85648800 is 884658.

It is not an unprimeable number, because it can be changed into a prime (85648807) by changing a digit.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 304660 + ... + 304940.

It is an arithmetic number, because the mean of its divisors is an integer number (1958208).

Almost surely, 2^85648800 is an apocalyptic number.

85648800 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 85648800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (140990976).

85648800 is an abundant number, since it is smaller than the sum of its proper divisors (196333152).

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

85648800 is a wasteful number, since it uses less digits than its factorization.

85648800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 431 (or 418 counting only the distinct ones).

The product of its (nonzero) digits is 61440, while the sum is 39.

The square root of 85648800 is about 9254.6636891894. The cubic root of 85648800 is about 440.7988243310.

The spelling of 85648800 in words is "eighty-five million, six hundred forty-eight thousand, eight hundred".