338688 has 108 divisors (see below), whose sum is σ = 1165080. Its totient is φ = 96768.

The previous prime is 338687. The next prime is 338707. The reversal of 338688 is 886833.

It is a powerful number, because all its prime factors have an exponent greater than 1 and also an Achilles number because it is not a perfect power.

338688 is digitally balanced in base 3, because in such base it contains all the possibile digits an equal number of times.

It is a tau number, because it is divible by the number of its divisors (108).

It is a super-2 number, since 2×338688² = 229419122688, which contains 22 as substring.

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

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

Its product of digits (27648) is a multiple of the sum of its prime divisors (12).

It is not an unprimeable number, because it can be changed into a prime (338683) by changing a digit.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 48381 + ... + 48387.

2³³⁸⁶⁸⁸ 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 338688, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (582540).

338688 is an abundant number, since it is smaller than the sum of its proper divisors (826392).

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

338688 is an equidigital number, since it uses as much as digits as its factorization.

338688 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 39 (or 12 counting only the distinct ones).

The product of its digits is 27648, while the sum is 36.

The square root of 338688 is about 581.9690713431. The cubic root of 338688 is about 69.7054288028.

Adding to 338688 its sum of digits (36), we get a square (338724 = 582²).

Multiplying 338688 by its product of digits (27648), we get a square (9364045824 = 96768²).

The spelling of 338688 in words is "three hundred thirty-eight thousand, six hundred eighty-eight".