What are the divisors of 2110?

1, 2, 5, 10, 211, 422, 1055, 2110

There is a total of 8 positive divisors.
The sum of these divisors is 3816.
The arithmetic mean is 477.

4 even divisors

2, 10, 422, 2110

4 odd divisors

1, 5, 211, 1055

How to compute the divisors of 2110?

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 2110 by each of the numbers from 1 to 2110 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)

2110 / 1 = 2110 (the remainder is 0, so 1 is a divisor of 2110)
2110 / 2 = 1055 (the remainder is 0, so 2 is a divisor of 2110)
2110 / 3 = 703.33333333333 (the remainder is 1, so 3 is not a divisor of 2110)
...
2110 / 2109 = 1.0004741583689 (the remainder is 1, so 2109 is not a divisor of 2110)
2110 / 2110 = 1 (the remainder is 0, so 2110 is a divisor of 2110)

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 2110 (i.e. 45.934736311423). 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 $\frac{N}{d} = D$ )

2110 / 1 = 2110 (the remainder is 0, so 1 and 2110 are divisors of 2110)
2110 / 2 = 1055 (the remainder is 0, so 2 and 1055 are divisors of 2110)
2110 / 3 = 703.33333333333 (the remainder is 1, so 3 is not a divisor of 2110)
...
2110 / 44 = 47.954545454545 (the remainder is 42, so 44 is not a divisor of 2110)
2110 / 45 = 46.888888888889 (the remainder is 40, so 45 is not a divisor of 2110)