What are the divisors of 9110?

1, 2, 5, 10, 911, 1822, 4555, 9110

There is a total of 8 positive divisors.
The sum of these divisors is 16416.
The arithmetic mean is 2052.

4 even divisors

2, 10, 1822, 9110

4 odd divisors

1, 5, 911, 4555

How to compute the divisors of 9110?

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 9110 by each of the numbers from 1 to 9110 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)

9110 / 1 = 9110 (the remainder is 0, so 1 is a divisor of 9110)
9110 / 2 = 4555 (the remainder is 0, so 2 is a divisor of 9110)
9110 / 3 = 3036.6666666667 (the remainder is 2, so 3 is not a divisor of 9110)
...
9110 / 9109 = 1.0001097815347 (the remainder is 1, so 9109 is not a divisor of 9110)
9110 / 9110 = 1 (the remainder is 0, so 9110 is a divisor of 9110)

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 9110 (i.e. 95.44631999192). 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 $\frac{N}{d} = D$ )

9110 / 1 = 9110 (the remainder is 0, so 1 and 9110 are divisors of 9110)
9110 / 2 = 4555 (the remainder is 0, so 2 and 4555 are divisors of 9110)
9110 / 3 = 3036.6666666667 (the remainder is 2, so 3 is not a divisor of 9110)
...
9110 / 94 = 96.914893617021 (the remainder is 86, so 94 is not a divisor of 9110)
9110 / 95 = 95.894736842105 (the remainder is 85, so 95 is not a divisor of 9110)