684096000 has 320 divisors, whose sum is σ = 2604476160. Its totient is φ = 156057600.

The previous prime is 684095999. The next prime is 684096013. The reversal of 684096000 is 690486.

It is a tau number, because it is divible by the number of its divisors (320).

It is an unprimeable number.

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 31 ways as a sum of consecutive naturals, for example, 1343746 + ... + 1344254.

It is an arithmetic number, because the mean of its divisors is an integer number (8138988).

Almost surely, 2^684096000 is an apocalyptic number.

684096000 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 684096000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1302238080).

684096000 is an abundant number, since it is smaller than the sum of its proper divisors (1920380160).

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

684096000 is an equidigital number, since it uses as much as digits as its factorization.

684096000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 552 (or 526 counting only the distinct ones).

The product of its (nonzero) digits is 10368, while the sum is 33.

The square root of 684096000 is about 26155.2289227221. The cubic root of 684096000 is about 881.1280299984.

The spelling of 684096000 in words is "six hundred eighty-four million, ninety-six thousand".