688642560 has 360 divisors, whose sum is σ = 2536970436. Its totient is φ = 179159040.

The previous prime is 688642547. The next prime is 688642567. The reversal of 688642560 is 65246886.

688642560 is a `hidden beast` number, since 6 + 8 + 86 + 4 + 2 + 560 = 666.

It can be written as a sum of positive squares in 2 ways, for example, as 606341376 + 82301184 = 24624^2 + 9072^2 .

It is a tau number, because it is divible by the number of its divisors (360).

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

It is a Saint-Exupery number, since it is equal to the product of the sides of a Pythagorean triangle: 1476 × 324 × 1440.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (688642567) 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 35 ways as a sum of consecutive naturals, for example, 16796140 + ... + 16796180.

Almost surely, 2^688642560 is an apocalyptic number.

688642560 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 688642560, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1268485218).

688642560 is an abundant number, since it is smaller than the sum of its proper divisors (1848327876).

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

688642560 is an frugal number, since it uses more digits than its factorization.

688642560 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 88 (or 51 counting only the distinct ones).

The product of its (nonzero) digits is 552960, while the sum is 45.

The square root of 688642560 is about 26241.9999237863. Note that the first 4 decimals coincide. The cubic root of 688642560 is about 883.0757386616.

The spelling of 688642560 in words is "six hundred eighty-eight million, six hundred forty-two thousand, five hundred sixty".