86580 has 72 divisors (see below), whose sum is σ = 290472. Its totient is φ = 20736.

The previous prime is 86579. The next prime is 86587. The reversal of 86580 is 8568.

86580 is a `hidden beast` number, since 8 + 658 + 0 = 666.

It can be written as a sum of positive squares in 4 ways, for example, as 10404 + 76176 = 102^2 + 276^2 .

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (86587) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 2322 + ... + 2358.

2⁸⁶⁵⁸⁰ is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 86580, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (145236).

86580 is an abundant number, since it is smaller than the sum of its proper divisors (203892).

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

86580 is a wasteful number, since it uses less digits than its factorization.

86580 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 65 (or 60 counting only the distinct ones).

The product of its (nonzero) digits is 1920, while the sum is 27.

The square root of 86580 is about 294.2447960457. The cubic root of 86580 is about 44.2390569512.

It can be divided in two parts, 86 and 580, that added together give a palindrome (666).

The spelling of 86580 in words is "eighty-six thousand, five hundred eighty".