311688 has 80 divisors (see below), whose sum is σ = 965580. Its totient is φ = 93312.

The previous prime is 311687. The next prime is 311711. The reversal of 311688 is 886113.

It can be written as a sum of positive squares in 2 ways, for example, as 311364 + 324 = 558^2 + 18^2 .

It is a Harshad number since it is a multiple of its sum of digits (27).

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

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 311688.

It is not an unprimeable number, because it can be changed into a prime (311681) by changing a digit.

It is a polite number, since it can be written in 19 ways as a sum of consecutive naturals, for example, 8406 + ... + 8442.

2³¹¹⁶⁸⁸ 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 311688, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (482790).

311688 is an abundant number, since it is smaller than the sum of its proper divisors (653892).

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

311688 is a wasteful number, since it uses less digits than its factorization.

311688 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 68 (or 55 counting only the distinct ones).

The product of its digits is 1152, while the sum is 27.

The square root of 311688 is about 558.2902470937. The cubic root of 311688 is about 67.8016132438.

It can be divided in two parts, 311 and 688, that added together give a palindrome (999).

The spelling of 311688 in words is "three hundred eleven thousand, six hundred eighty-eight".