4164 has 12 divisors (see below), whose sum is σ = 9744. Its totient is φ = 1384.

The previous prime is 4159. The next prime is 4177. The reversal of 4164 is 4614.

Added to its reverse (4614) it gives a triangular number (8778 = T₁₃₂).

It is a tau number, because it is divible by the number of its divisors (12).

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

It is a plaindrome in base 15.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 4164.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (3) of ones.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 162 + ... + 185.

It is an arithmetic number, because the mean of its divisors is an integer number (812).

2⁴¹⁶⁴ is an apocalyptic number.

It is an amenable number.

4164 is an abundant number, since it is smaller than the sum of its proper divisors (5580).

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

It is a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (4872).

4164 is a wasteful number, since it uses less digits than its factorization.

4164 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 354 (or 352 counting only the distinct ones).

The product of its digits is 96, while the sum is 15.

The square root of 4164 is about 64.5290632196. The cubic root of 4164 is about 16.0880561597.

Adding to 4164 its reverse (4614), we get a palindrome (8778).

It can be divided in two parts, 41 and 64, that added together give a triangular number (105 = T₁₄).

The spelling of 4164 in words is "four thousand, one hundred sixty-four".