What are the divisors of 2118?

1, 2, 3, 6, 353, 706, 1059, 2118

There is a total of 8 positive divisors.
The sum of these divisors is 4248.
The arithmetic mean is 531.

4 even divisors

2, 6, 706, 2118

4 odd divisors

1, 3, 353, 1059

How to compute the divisors of 2118?

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 2118 by each of the numbers from 1 to 2118 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)

2118 / 1 = 2118 (the remainder is 0, so 1 is a divisor of 2118)
2118 / 2 = 1059 (the remainder is 0, so 2 is a divisor of 2118)
2118 / 3 = 706 (the remainder is 0, so 3 is a divisor of 2118)
...
2118 / 2117 = 1.0004723665564 (the remainder is 1, so 2117 is not a divisor of 2118)
2118 / 2118 = 1 (the remainder is 0, so 2118 is a divisor of 2118)

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 2118 (i.e. 46.021733996015). 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 $\frac{N}{d} = D$ )

2118 / 1 = 2118 (the remainder is 0, so 1 and 2118 are divisors of 2118)
2118 / 2 = 1059 (the remainder is 0, so 2 and 1059 are divisors of 2118)
2118 / 3 = 706 (the remainder is 0, so 3 and 706 are divisors of 2118)
...
2118 / 45 = 47.066666666667 (the remainder is 3, so 45 is not a divisor of 2118)
2118 / 46 = 46.04347826087 (the remainder is 2, so 46 is not a divisor of 2118)