688640 has 40 divisors (see below), whose sum is σ = 1657260. Its totient is φ = 274432.

The previous prime is 688637. The next prime is 688657. The reversal of 688640 is 46886.

It can be written as a sum of positive squares in 2 ways, for example, as 614656 + 73984 = 784^2 + 272^2 .

It is a tau number, because it is divible by the number of its divisors (40).

It is a Harshad number since it is a multiple of its sum of digits (32).

It is a nialpdrome in base 16.

It is a junction number, because it is equal to n+sod(n) for n = 688597 and 688606.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 688640.

It is an unprimeable number.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 2426 + ... + 2694.

2⁶⁸⁸⁶⁴⁰ is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 688640, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (828630).

688640 is an abundant number, since it is smaller than the sum of its proper divisors (968620).

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

688640 is an equidigital number, since it uses as much as digits as its factorization.

688640 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 292 (or 276 counting only the distinct ones).

The product of its (nonzero) digits is 9216, while the sum is 32.

The square root of 688640 is about 829.8433587130. The cubic root of 688640 is about 88.3074644395.

The spelling of 688640 in words is "six hundred eighty-eight thousand, six hundred forty".