208164 has 48 divisors (see below), whose sum is σ = 564480. Its totient is φ = 59040.

The previous prime is 208147. The next prime is 208189. The reversal of 208164 is 461802.

It is a self number, because there is not a number n which added to its sum of digits gives 208164.

It is an unprimeable number.

208164 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, 2467 + ... + 2549.

It is an arithmetic number, because the mean of its divisors is an integer number (11760).

2²⁰⁸¹⁶⁴ 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 208164, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (282240).

208164 is an abundant number, since it is smaller than the sum of its proper divisors (356316).

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

208164 is a wasteful number, since it uses less digits than its factorization.

208164 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 120 (or 118 counting only the distinct ones).

The product of its (nonzero) digits is 384, while the sum is 21.

The square root of 208164 is about 456.2499315068. The cubic root of 208164 is about 59.2654893720.

Adding to 208164 its reverse (461802), we get a palindrome (669966).

It can be divided in two parts, 2081 and 64, that added together give a triangular number (2145 = T₆₅).

The spelling of 208164 in words is "two hundred eight thousand, one hundred sixty-four".