268584 has 48 divisors (see below), whose sum is σ = 731520. Its totient is φ = 82080.

The previous prime is 268573. The next prime is 268607. The reversal of 268584 is 485862.

It is a Smith number, since the sum of its digits (33) 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 11 ways as a sum of consecutive naturals, for example, 8649 + ... + 8679.

It is an arithmetic number, because the mean of its divisors is an integer number (15240).

2²⁶⁸⁵⁸⁴ is an apocalyptic number.

268584 is a gapful number since it is divisible by the number (24) 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 268584, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (365760).

268584 is an abundant number, since it is smaller than the sum of its proper divisors (462936).

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

268584 is a wasteful number, since it uses less digits than its factorization.

268584 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 78 (or 55 counting only the distinct ones).

The product of its digits is 15360, while the sum is 33.

The square root of 268584 is about 518.2509044855. The cubic root of 268584 is about 64.5198544730.

It can be divided in two parts, 26858 and 4, that added together give a palindrome (26862).

The spelling of 268584 in words is "two hundred sixty-eight thousand, five hundred eighty-four".