What are the divisors of 1118?

1, 2, 13, 26, 43, 86, 559, 1118

There is a total of 8 positive divisors.
The sum of these divisors is 1848.
The arithmetic mean is 231.

4 even divisors

2, 26, 86, 1118

4 odd divisors

1, 13, 43, 559

How to compute the divisors of 1118?

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 1118 by each of the numbers from 1 to 1118 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)

1118 / 1 = 1118 (the remainder is 0, so 1 is a divisor of 1118)
1118 / 2 = 559 (the remainder is 0, so 2 is a divisor of 1118)
1118 / 3 = 372.66666666667 (the remainder is 2, so 3 is not a divisor of 1118)
...
1118 / 1117 = 1.0008952551477 (the remainder is 1, so 1117 is not a divisor of 1118)
1118 / 1118 = 1 (the remainder is 0, so 1118 is a divisor of 1118)

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 1118 (i.e. 33.436506994601). 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 $\frac{N}{d} = D$ )

1118 / 1 = 1118 (the remainder is 0, so 1 and 1118 are divisors of 1118)
1118 / 2 = 559 (the remainder is 0, so 2 and 559 are divisors of 1118)
1118 / 3 = 372.66666666667 (the remainder is 2, so 3 is not a divisor of 1118)
...
1118 / 32 = 34.9375 (the remainder is 30, so 32 is not a divisor of 1118)
1118 / 33 = 33.878787878788 (the remainder is 29, so 33 is not a divisor of 1118)