What are the divisors of 2166?

1, 2, 3, 6, 19, 38, 57, 114, 361, 722, 1083, 2166

There is a total of 12 positive divisors.
The sum of these divisors is 4572.
The arithmetic mean is 381.

6 even divisors

2, 6, 38, 114, 722, 2166

6 odd divisors

1, 3, 19, 57, 361, 1083

How to compute the divisors of 2166?

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 2166 by each of the numbers from 1 to 2166 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)

2166 / 1 = 2166 (the remainder is 0, so 1 is a divisor of 2166)
2166 / 2 = 1083 (the remainder is 0, so 2 is a divisor of 2166)
2166 / 3 = 722 (the remainder is 0, so 3 is a divisor of 2166)
...
2166 / 2165 = 1.0004618937644 (the remainder is 1, so 2165 is not a divisor of 2166)
2166 / 2166 = 1 (the remainder is 0, so 2166 is a divisor of 2166)

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 2166 (i.e. 46.54030511288). 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 $\frac{N}{d} = D$ )

2166 / 1 = 2166 (the remainder is 0, so 1 and 2166 are divisors of 2166)
2166 / 2 = 1083 (the remainder is 0, so 2 and 1083 are divisors of 2166)
2166 / 3 = 722 (the remainder is 0, so 3 and 722 are divisors of 2166)
...
2166 / 45 = 48.133333333333 (the remainder is 6, so 45 is not a divisor of 2166)
2166 / 46 = 47.086956521739 (the remainder is 4, so 46 is not a divisor of 2166)