688644 has 72 divisors (see below), whose sum is σ = 1991808. Its totient is φ = 198720.

The previous prime is 688637. The next prime is 688657. The reversal of 688644 is 446886.

688644 is a `hidden beast` number, since 6 + 8 + 8 + 644 = 666.

It is a Harshad number since it is a multiple of its sum of digits (36).

It is a junction number, because it is equal to n+sod(n) for n = 688599 and 688608.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (5) of ones.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 14629 + ... + 14675.

It is an arithmetic number, because the mean of its divisors is an integer number (27664).

2⁶⁸⁸⁶⁴⁴ 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 688644, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (995904).

688644 is an abundant number, since it is smaller than the sum of its proper divisors (1303164).

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

688644 is a wasteful number, since it uses less digits than its factorization.

688644 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 105 (or 100 counting only the distinct ones).

The product of its digits is 36864, while the sum is 36.

The square root of 688644 is about 829.8457688029. The cubic root of 688644 is about 88.3076354186.

The spelling of 688644 in words is "six hundred eighty-eight thousand, six hundred forty-four".