688116 has 48 divisors (see below), whose sum is σ = 1891008. Its totient is φ = 192000.

The previous prime is 688111. The next prime is 688133. The reversal of 688116 is 611886.

It is an Ulam number.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (688111) by changing a digit.

688116 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 1516 + ... + 1916.

It is an arithmetic number, because the mean of its divisors is an integer number (39396).

2⁶⁸⁸¹¹⁶ is an apocalyptic number.

688116 is a gapful number since it is divisible by the number (66) 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 688116, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (945504).

688116 is an abundant number, since it is smaller than the sum of its proper divisors (1202892).

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

688116 is a wasteful number, since it uses less digits than its factorization.

688116 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 432 (or 430 counting only the distinct ones).

The product of its digits is 2304, while the sum is 30.

The square root of 688116 is about 829.5275763951. The cubic root of 688116 is about 88.2850604485.

The spelling of 688116 in words is "six hundred eighty-eight thousand, one hundred sixteen".