681984000 has 360 divisors, whose sum is σ = 2525156088. Its totient is φ = 176947200.

The previous prime is 681983993. The next prime is 681984071. The reversal of 681984000 is 489186.

It is a happy number.

681984000 is a `hidden beast` number, since 68 + 198 + 400 + 0 = 666.

It can be written as a sum of positive squares in 4 ways, for example, as 147456 + 681836544 = 384^2 + 26112^2 .

It is a tau number, because it is divible by the number of its divisors (360).

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

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 18431982 + ... + 18432018.

Almost surely, 2^681984000 is an apocalyptic number.

681984000 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 681984000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1262578044).

681984000 is an abundant number, since it is smaller than the sum of its proper divisors (1843172088).

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

681984000 is an equidigital number, since it uses as much as digits as its factorization.

681984000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 86 (or 47 counting only the distinct ones).

The product of its (nonzero) digits is 13824, while the sum is 36.

The square root of 681984000 is about 26114.8233767721. The cubic root of 681984000 is about 880.2203305050.

The spelling of 681984000 in words is "six hundred eighty-one million, nine hundred eighty-four thousand".