85984800 has 144 divisors (see below), whose sum is σ = 305417952. Its totient is φ = 20838400.

The previous prime is 85984783. The next prime is 85984817. The reversal of 85984800 is 848958.

It is an interprime number because it is at equal distance from previous prime (85984783) and next prime (85984817).

It is a Smith number, since the sum of its digits (42) coincides with the sum of the digits of its prime factors.

It is an unprimeable number.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 24772 + ... + 28028.

It is an arithmetic number, because the mean of its divisors is an integer number (2120958).

Almost surely, 2^85984800 is an apocalyptic number.

85984800 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 85984800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (152708976).

85984800 is an abundant number, since it is smaller than the sum of its proper divisors (219433152).

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

85984800 is a wasteful number, since it uses less digits than its factorization.

85984800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 3291 (or 3278 counting only the distinct ones).

The product of its (nonzero) digits is 92160, while the sum is 42.

The square root of 85984800 is about 9272.7989302044. The cubic root of 85984800 is about 441.3744897215.

The spelling of 85984800 in words is "eighty-five million, nine hundred eighty-four thousand, eight hundred".