What are the divisors of 9116?

1, 2, 4, 43, 53, 86, 106, 172, 212, 2279, 4558, 9116

There is a total of 12 positive divisors.
The sum of these divisors is 16632.
The arithmetic mean is 1386.

8 even divisors

2, 4, 86, 106, 172, 212, 4558, 9116

4 odd divisors

1, 43, 53, 2279

How to compute the divisors of 9116?

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 9116 by each of the numbers from 1 to 9116 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)

9116 / 1 = 9116 (the remainder is 0, so 1 is a divisor of 9116)
9116 / 2 = 4558 (the remainder is 0, so 2 is a divisor of 9116)
9116 / 3 = 3038.6666666667 (the remainder is 2, so 3 is not a divisor of 9116)
...
9116 / 9115 = 1.0001097092704 (the remainder is 1, so 9115 is not a divisor of 9116)
9116 / 9116 = 1 (the remainder is 0, so 9116 is a divisor of 9116)

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 9116 (i.e. 95.47774609824). 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 $\frac{N}{d} = D$ )

9116 / 1 = 9116 (the remainder is 0, so 1 and 9116 are divisors of 9116)
9116 / 2 = 4558 (the remainder is 0, so 2 and 4558 are divisors of 9116)
9116 / 3 = 3038.6666666667 (the remainder is 2, so 3 is not a divisor of 9116)
...
9116 / 94 = 96.978723404255 (the remainder is 92, so 94 is not a divisor of 9116)
9116 / 95 = 95.957894736842 (the remainder is 91, so 95 is not a divisor of 9116)