685584000 has 480 divisors, whose sum is σ = 2661799140. Its totient is φ = 174873600.

The previous prime is 685583993. The next prime is 685584013. The reversal of 685584000 is 485586.

It is a happy number.

It is a powerful number, because all its prime factors have an exponent greater than 1 and also an Achilles number because it is not a perfect power.

685584000 is a `hidden beast` number, since 68 + 558 + 40 + 0 + 0 = 666.

It can be written as a sum of positive squares in 2 ways, for example, as 463454784 + 222129216 = 21528^2 + 14904^2 .

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 an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 59 ways as a sum of consecutive naturals, for example, 29807989 + ... + 29808011.

Almost surely, 2^685584000 is an apocalyptic number.

685584000 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 685584000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1330899570).

685584000 is an abundant number, since it is smaller than the sum of its proper divisors (1976215140).

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

685584000 is an equidigital number, since it uses as much as digits as its factorization.

685584000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 87 (or 33 counting only the distinct ones).

The product of its (nonzero) digits is 38400, while the sum is 36.

The square root of 685584000 is about 26183.6590261942. The cubic root of 685584000 is about 881.7664243351.

The spelling of 685584000 in words is "six hundred eighty-five million, five hundred eighty-four thousand".