688224 has 48 divisors (see below), whose sum is σ = 1850688. Its totient is φ = 223872.

The previous prime is 688223. The next prime is 688249. The reversal of 688224 is 422886.

It is a happy number.

It is a tau number, because it is divible by the number of its divisors (48).

It is a nude number because it is divisible by every one of its digits.

It is a junction number, because it is equal to n+sod(n) for n = 688191 and 688200.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (688223) by changing a digit.

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

It is an upside-down number.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 6379 + ... + 6485.

It is an arithmetic number, because the mean of its divisors is an integer number (38556).

2⁶⁸⁸²²⁴ 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 688224, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (925344).

688224 is an abundant number, since it is smaller than the sum of its proper divisors (1162464).

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

688224 is a wasteful number, since it uses less digits than its factorization.

688224 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 187 (or 179 counting only the distinct ones).

The product of its digits is 6144, while the sum is 30.

The square root of 688224 is about 829.5926711345. The cubic root of 688224 is about 88.2896789952.

The spelling of 688224 in words is "six hundred eighty-eight thousand, two hundred twenty-four".