684864000 has 480 divisors, whose sum is σ = 2614051440. Its totient is φ = 172032000.

The previous prime is 684863983. The next prime is 684864001. The reversal of 684864000 is 468486.

684864000 is a `hidden beast` number, since 6 + 8 + 4 + 8 + 640 + 0 + 0 = 666.

It can be written as a sum of positive squares in 8 ways, for example, as 5531904 + 679332096 = 2352^2 + 26064^2 .

It is a tau number, because it is divible by the number of its divisors (480).

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

It is not an unprimeable number, because it can be changed into a prime (684864001) by changing a digit.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 16703980 + ... + 16704020.

Almost surely, 2^684864000 is an apocalyptic number.

684864000 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 684864000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1307025720).

684864000 is an abundant number, since it is smaller than the sum of its proper divisors (1929187440).

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

684864000 is a wasteful number, since it uses less digits than its factorization.

684864000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 109 (or 80 counting only the distinct ones).

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

The square root of 684864000 is about 26169.9063811852. The cubic root of 684864000 is about 881.4576393174.

The spelling of 684864000 in words is "six hundred eighty-four million, eight hundred sixty-four thousand".