685728000 has 216 divisors, whose sum is σ = 2468485656. Its totient is φ = 182784000.

The previous prime is 685727969. The next prime is 685728007. The reversal of 685728000 is 827586.

685728000 is a `hidden beast` number, since 6 + 8 + 572 + 80 + 0 + 0 = 666.

It can be written as a sum of positive squares in 4 ways, for example, as 212926464 + 472801536 = 14592^2 + 21744^2 .

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 (685728007) by changing a digit.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 286810 + ... + 289190.

Almost surely, 2^685728000 is an apocalyptic number.

685728000 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 685728000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1234242828).

685728000 is an abundant number, since it is smaller than the sum of its proper divisors (1782757656).

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

685728000 is a wasteful number, since it uses less digits than its factorization.

685728000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 2418 (or 2391 counting only the distinct ones).

The product of its (nonzero) digits is 26880, while the sum is 36.

The square root of 685728000 is about 26186.4086884781. The cubic root of 685728000 is about 881.8281553927.

The spelling of 685728000 in words is "six hundred eighty-five million, seven hundred twenty-eight thousand".