What are the divisors of 9118?

1, 2, 47, 94, 97, 194, 4559, 9118

There is a total of 8 positive divisors.
The sum of these divisors is 14112.
The arithmetic mean is 1764.

4 even divisors

2, 94, 194, 9118

4 odd divisors

1, 47, 97, 4559

How to compute the divisors of 9118?

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 9118 by each of the numbers from 1 to 9118 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)

9118 / 1 = 9118 (the remainder is 0, so 1 is a divisor of 9118)
9118 / 2 = 4559 (the remainder is 0, so 2 is a divisor of 9118)
9118 / 3 = 3039.3333333333 (the remainder is 1, so 3 is not a divisor of 9118)
...
9118 / 9117 = 1.0001096852035 (the remainder is 1, so 9117 is not a divisor of 9118)
9118 / 9118 = 1 (the remainder is 0, so 9118 is a divisor of 9118)

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 9118 (i.e. 95.488219168649). 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 $\frac{N}{d} = D$ )

9118 / 1 = 9118 (the remainder is 0, so 1 and 9118 are divisors of 9118)
9118 / 2 = 4559 (the remainder is 0, so 2 and 4559 are divisors of 9118)
9118 / 3 = 3039.3333333333 (the remainder is 1, so 3 is not a divisor of 9118)
...
9118 / 94 = 97 (the remainder is 0, so 94 and 97 are divisors of 9118)
9118 / 95 = 95.978947368421 (the remainder is 93, so 95 is not a divisor of 9118)