688349145600 has 1200 divisors, whose sum is σ = 2720473066080. Its totient is φ = 171395481600.

The previous prime is 688349145593. The next prime is 688349145611. The reversal of 688349145600 is 6541943886.

688349145600 is a `hidden beast` number, since 68 + 8 + 3 + 4 + 9 + 14 + 560 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (1200).

It is a Harshad number since it is a multiple of its sum of digits (54).

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 119 ways as a sum of consecutive naturals, for example, 1635033390 + ... + 1635033810.

Almost surely, 2^688349145600 is an apocalyptic number.

688349145600 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 688349145600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1360236533040).

688349145600 is an abundant number, since it is smaller than the sum of its proper divisors (2032123920480).

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

688349145600 is a wasteful number, since it uses less digits than its factorization.

688349145600 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 563 (or 533 counting only the distinct ones).

The product of its (nonzero) digits is 4976640, while the sum is 54.

The spelling of 688349145600 in words is "six hundred eighty-eight billion, three hundred forty-nine million, one hundred forty-five thousand, six hundred".