82784 has 24 divisors (see below), whose sum is σ = 176400. Its totient is φ = 38016.

The previous prime is 82781. The next prime is 82787. The reversal of 82784 is 48728.

It is an interprime number because it is at equal distance from previous prime (82781) and next prime (82787).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (82781) by changing a digit.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 317 + ... + 515.

It is an arithmetic number, because the mean of its divisors is an integer number (7350).

2⁸²⁷⁸⁴ 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 82784, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (88200).

82784 is an abundant number, since it is smaller than the sum of its proper divisors (93616).

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

82784 is a wasteful number, since it uses less digits than its factorization.

82784 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 222 (or 214 counting only the distinct ones).

The product of its digits is 3584, while the sum is 29.

The square root of 82784 is about 287.7220881337. The cubic root of 82784 is about 43.5828341931.

Adding to 82784 its product of digits (3584), we get a palindrome (86368).

The spelling of 82784 in words is "eighty-two thousand, seven hundred eighty-four".