What are the divisors of 8110?

1, 2, 5, 10, 811, 1622, 4055, 8110

There is a total of 8 positive divisors.
The sum of these divisors is 14616.
The arithmetic mean is 1827.

4 even divisors

2, 10, 1622, 8110

4 odd divisors

1, 5, 811, 4055

How to compute the divisors of 8110?

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 8110 by each of the numbers from 1 to 8110 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)

8110 / 1 = 8110 (the remainder is 0, so 1 is a divisor of 8110)
8110 / 2 = 4055 (the remainder is 0, so 2 is a divisor of 8110)
8110 / 3 = 2703.3333333333 (the remainder is 1, so 3 is not a divisor of 8110)
...
8110 / 8109 = 1.0001233197682 (the remainder is 1, so 8109 is not a divisor of 8110)
8110 / 8110 = 1 (the remainder is 0, so 8110 is a divisor of 8110)

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 8110 (i.e. 90.055538419355). 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 $\frac{N}{d} = D$ )

8110 / 1 = 8110 (the remainder is 0, so 1 and 8110 are divisors of 8110)
8110 / 2 = 4055 (the remainder is 0, so 2 and 4055 are divisors of 8110)
8110 / 3 = 2703.3333333333 (the remainder is 1, so 3 is not a divisor of 8110)
...
8110 / 89 = 91.123595505618 (the remainder is 11, so 89 is not a divisor of 8110)
8110 / 90 = 90.111111111111 (the remainder is 10, so 90 is not a divisor of 8110)