684000 has 144 divisors (see below), whose sum is σ = 2555280. Its totient is φ = 172800.

The previous prime is 683983. The next prime is 684007. The reversal of 684000 is 486.

It is a tau number, because it is divible by the number of its divisors (144).

It is a Harshad number since it is a multiple of its sum of digits (18).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (684007) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 35991 + ... + 36009.

It is an arithmetic number, because the mean of its divisors is an integer number (17745).

2⁶⁸⁴⁰⁰⁰ is an apocalyptic number.

684000 is a gapful number since it is divisible by the number (60) 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 684000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1277640).

684000 is an abundant number, since it is smaller than the sum of its proper divisors (1871280).

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

684000 is a wasteful number, since it uses less digits than its factorization.

684000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 50 (or 29 counting only the distinct ones).

The product of its (nonzero) digits is 192, while the sum is 18.

The square root of 684000 is about 827.0429251254. The cubic root of 684000 is about 88.1086811491.

Adding to 684000 its reverse (486), we get a palindrome (684486).

The spelling of 684000 in words is "six hundred eighty-four thousand".