688138560 has 168 divisors, whose sum is σ = 2406325896. Its totient is φ = 180449280.

The previous prime is 688138531. The next prime is 688138601. The reversal of 688138560 is 65831886.

688138560 is a `hidden beast` number, since 6 + 8 + 81 + 3 + 8 + 560 = 666.

It can be written as a sum of positive squares in 4 ways, for example, as 23736384 + 664402176 = 4872^2 + 25776^2 .

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

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 173722 + ... + 177638.

Almost surely, 2^688138560 is an apocalyptic number.

688138560 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 688138560, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1203162948).

688138560 is an abundant number, since it is smaller than the sum of its proper divisors (1718187336).

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

688138560 is a wasteful number, since it uses less digits than its factorization.

688138560 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 4001 (or 3988 counting only the distinct ones).

The product of its (nonzero) digits is 276480, while the sum is 45.

The square root of 688138560 is about 26232.3952394744. The cubic root of 688138560 is about 882.8602525150.

The spelling of 688138560 in words is "six hundred eighty-eight million, one hundred thirty-eight thousand, five hundred sixty".