688896000 has 576 divisors, whose sum is σ = 2790365760. Its totient is φ = 162201600.

The previous prime is 688895993. The next prime is 688896001. The reversal of 688896000 is 698886.

It is a tau number, because it is divible by the number of its divisors (576).

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

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (688896001) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 29951989 + ... + 29952011.

It is an arithmetic number, because the mean of its divisors is an integer number (4844385).

Almost surely, 2^688896000 is an apocalyptic number.

688896000 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 688896000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1395182880).

688896000 is an abundant number, since it is smaller than the sum of its proper divisors (2101469760).

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

688896000 is a wasteful number, since it uses less digits than its factorization.

688896000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 79 (or 46 counting only the distinct ones).

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

The square root of 688896000 is about 26246.8283798252. The cubic root of 688896000 is about 883.1840576832.

The spelling of 688896000 in words is "six hundred eighty-eight million, eight hundred ninety-six thousand".