688089600 has 480 divisors, whose sum is σ = 2770447680. Its totient is φ = 165888000.

The previous prime is 688089587. The next prime is 688089601. The reversal of 688089600 is 6980886.

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 (45).

It is not an unprimeable number, because it can be changed into a prime (688089601) by changing a digit.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 3801510 + ... + 3801690.

It is an arithmetic number, because the mean of its divisors is an integer number (5771766).

Almost surely, 2^688089600 is an apocalyptic number.

688089600 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 688089600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1385223840).

688089600 is an abundant number, since it is smaller than the sum of its proper divisors (2082358080).

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

688089600 is a wasteful number, since it uses less digits than its factorization.

688089600 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 229 (or 202 counting only the distinct ones).

The product of its (nonzero) digits is 165888, while the sum is 45.

The square root of 688089600 is about 26231.4620255906. The cubic root of 688089600 is about 882.8393139688.

The spelling of 688089600 in words is "six hundred eighty-eight million, eighty-nine thousand, six hundred".