164688 has 40 divisors (see below), whose sum is σ = 440448. Its totient is φ = 52992.

The previous prime is 164683. The next prime is 164701. The reversal of 164688 is 886461.

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

It is a congruent number.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 164688.

It is not an unprimeable number, because it can be changed into a prime (164683) by changing a digit.

164688 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 7 ways as a sum of consecutive naturals, for example, 2220 + ... + 2292.

2¹⁶⁴⁶⁸⁸ 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 164688, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (220224).

164688 is an abundant number, since it is smaller than the sum of its proper divisors (275760).

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

164688 is a wasteful number, since it uses less digits than its factorization.

164688 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 131 (or 125 counting only the distinct ones).

The product of its digits is 9216, while the sum is 33.

The square root of 164688 is about 405.8176930593. The cubic root of 164688 is about 54.8134728094.

The spelling of 164688 in words is "one hundred sixty-four thousand, six hundred eighty-eight".