86580800 has 84 divisors (see below), whose sum is σ = 217275156. Its totient is φ = 33945600.

The previous prime is 86580797. The next prime is 86580803. The reversal of 86580800 is 808568.

It is an interprime number because it is at equal distance from previous prime (86580797) and next prime (86580803).

It can be written as a sum of positive squares in 6 ways, for example, as 16384 + 86564416 = 128^2 + 9304^2 .

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (86580803) by changing a digit.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 84290 + ... + 85310.

It is an arithmetic number, because the mean of its divisors is an integer number (2586609).

Almost surely, 2^86580800 is an apocalyptic number.

86580800 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 86580800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (108637578).

86580800 is an abundant number, since it is smaller than the sum of its proper divisors (130694356).

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

86580800 is a wasteful number, since it uses less digits than its factorization.

86580800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 1096 (or 1081 counting only the distinct ones).

The product of its (nonzero) digits is 15360, while the sum is 35.

The square root of 86580800 is about 9304.8804398552. The cubic root of 86580800 is about 442.3919320720.

The spelling of 86580800 in words is "eighty-six million, five hundred eighty thousand, eight hundred".