What are the divisors of 2164?

1, 2, 4, 541, 1082, 2164

There is a total of 6 positive divisors.
The sum of these divisors is 3794.
The arithmetic mean is 632.33333333333.

4 even divisors

2, 4, 1082, 2164

2 odd divisors

1, 541

How to compute the divisors of 2164?

A number N is said to be divisible by a number M (with M non-zero) if, when we divide N by M, the remainder of the division is zero.

$N mod M = 0$

Brute force algorithm

We could start by using a brute-force method which would involve dividing 2164 by each of the numbers from 1 to 2164 to determine which ones have a remainder equal to 0.

$Remainder = N - (M \times ⌊ \frac{N}{M} ⌋)$

(where $⌊ \frac{N}{M} ⌋$ is the integer part of the quotient)

2164 / 1 = 2164 (the remainder is 0, so 1 is a divisor of 2164)
2164 / 2 = 1082 (the remainder is 0, so 2 is a divisor of 2164)
2164 / 3 = 721.33333333333 (the remainder is 1, so 3 is not a divisor of 2164)
...
2164 / 2163 = 1.0004623208507 (the remainder is 1, so 2163 is not a divisor of 2164)
2164 / 2164 = 1 (the remainder is 0, so 2164 is a divisor of 2164)

Improved algorithm using square-root

However, there is another slightly better approach that reduces the number of iterations by testing only integers less than or equal to the square root of 2164 (i.e. 46.518813398452). Indeed, if a number N has a divisor D greater than its square root, then there is necessarily a smaller divisor d such that:

$D \times d = N$

(thus, if $\frac{N}{D} = d$ , then $\frac{N}{d} = D$ )

2164 / 1 = 2164 (the remainder is 0, so 1 and 2164 are divisors of 2164)
2164 / 2 = 1082 (the remainder is 0, so 2 and 1082 are divisors of 2164)
2164 / 3 = 721.33333333333 (the remainder is 1, so 3 is not a divisor of 2164)
...
2164 / 45 = 48.088888888889 (the remainder is 4, so 45 is not a divisor of 2164)
2164 / 46 = 47.04347826087 (the remainder is 2, so 46 is not a divisor of 2164)