688128000 has 304 divisors, whose sum is σ = 2617240704. Its totient is φ = 157286400.

The previous prime is 688127983. The next prime is 688128019. The reversal of 688128000 is 821886.

It is an unprimeable number.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 98303997 + ... + 98304003.

Almost surely, 2^688128000 is an apocalyptic number.

688128000 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 688128000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1308620352).

688128000 is an abundant number, since it is smaller than the sum of its proper divisors (1929112704).

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

688128000 is an frugal number, since it uses more digits than its factorization.

688128000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 61 (or 17 counting only the distinct ones).

The product of its (nonzero) digits is 6144, while the sum is 33.

The square root of 688128000 is about 26232.1939608566. The cubic root of 688128000 is about 882.8557364420.

Adding to 688128000 its reverse (821886), we get a palindrome (688949886).

The spelling of 688128000 in words is "six hundred eighty-eight million, one hundred twenty-eight thousand".