684864 has 84 divisors (see below), whose sum is σ = 2080260. Its totient is φ = 215040.

The previous prime is 684857. The next prime is 684869. The reversal of 684864 is 468486.

It can be written as a sum of positive squares in 2 ways, for example, as 166464 + 518400 = 408^2 + 720^2 .

It is a Harshad number since it is a multiple of its sum of digits (36).

It is a nude number because it is divisible by every one of its digits.

It is a congruent number.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 684864.

It is not an unprimeable number, because it can be changed into a prime (684869) 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, 16684 + ... + 16724.

It is an arithmetic number, because the mean of its divisors is an integer number (24765).

2⁶⁸⁴⁸⁶⁴ is an apocalyptic number.

684864 is a gapful number since it is divisible by the number (64) 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 684864, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1040130).

684864 is an abundant number, since it is smaller than the sum of its proper divisors (1395396).

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

684864 is a wasteful number, since it uses less digits than its factorization.

684864 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 88 (or 75 counting only the distinct ones).

The product of its digits is 36864, while the sum is 36.

The square root of 684864 is about 827.5651031792. The cubic root of 684864 is about 88.1457639317.

The spelling of 684864 in words is "six hundred eighty-four thousand, eight hundred sixty-four".