12688 has 20 divisors (see below), whose sum is σ = 26908. Its totient is φ = 5760.

The previous prime is 12671. The next prime is 12689. The reversal of 12688 is 88621.

12688 is nontrivially palindromic in base 3.

It can be written as a sum of positive squares in 2 ways, for example, as 1024 + 11664 = 32^2 + 108^2 .

12688 is an undulating number in base 11.

It is a plaindrome in base 10.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (12689) by changing a digit.

12688 is an untouchable number, because it is not equal to the sum of proper divisors of any 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 3 ways as a sum of consecutive naturals, for example, 178 + ... + 238.

2¹²⁶⁸⁸ 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 12688, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (13454).

12688 is an abundant number, since it is smaller than the sum of its proper divisors (14220).

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

12688 is a wasteful number, since it uses less digits than its factorization.

12688 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 82 (or 76 counting only the distinct ones).

The product of its digits is 768, while the sum is 25.

The square root of 12688 is about 112.6410227226. The cubic root of 12688 is about 23.3237148565.

Adding to 12688 its product of digits (768), we get a square (13456 = 116²).

It can be divided in two parts, 12 and 688, that multiplied together give a triangular number (8256 = T₁₂₈).

The spelling of 12688 in words is "twelve thousand, six hundred eighty-eight".