684806400 has 270 divisors, whose sum is σ = 2533958042. Its totient is φ = 182476800.

The previous prime is 684806389. The next prime is 684806413. The reversal of 684806400 is 4608486.

684806400 is a `hidden beast` number, since 6 + 8 + 4 + 8 + 0 + 640 + 0 = 666.

It can be written as a sum of positive squares in 3 ways, for example, as 160579584 + 524226816 = 12672^2 + 22896^2 .

It is a tau number, because it is divible by the number of its divisors (270).

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

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 29 ways as a sum of consecutive naturals, for example, 517740 + ... + 519060.

Almost surely, 2^684806400 is an apocalyptic number.

684806400 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 684806400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1266979021).

684806400 is an abundant number, since it is smaller than the sum of its proper divisors (1849151642).

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

684806400 is a wasteful number, since it uses less digits than its factorization.

684806400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1359 (or 1331 counting only the distinct ones).

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

The square root of 684806400 is about 26168.8058573562. The cubic root of 684806400 is about 881.4329271685.

The spelling of 684806400 in words is "six hundred eighty-four million, eight hundred six thousand, four hundred".