688564800 has 1008 divisors, whose sum is σ = 3301788672. Its totient is φ = 136857600.

The previous prime is 688564781. The next prime is 688564801. The reversal of 688564800 is 8465886.

688564800 is a `hidden beast` number, since 6 + 8 + 8 + 564 + 80 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (1008).

It is a Harshad number since it is a multiple of its sum of digits (45).

It is not an unprimeable number, because it can be changed into a prime (688564801) by changing a digit.

It is a polite number, since it can be written in 143 ways as a sum of consecutive naturals, for example, 29937589 + ... + 29937611.

It is an arithmetic number, because the mean of its divisors is an integer number (3275584).

Almost surely, 2^688564800 is an apocalyptic number.

688564800 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 688564800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1650894336).

688564800 is an abundant number, since it is smaller than the sum of its proper divisors (2613223872).

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

688564800 is a wasteful number, since it uses less digits than its factorization.

688564800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 78 (or 51 counting only the distinct ones).

The product of its (nonzero) digits is 368640, while the sum is 45.

The square root of 688564800 is about 26240.5182875644. The cubic root of 688564800 is about 883.0424990885.

The spelling of 688564800 in words is "six hundred eighty-eight million, five hundred sixty-four thousand, eight hundred".