What are the divisors of 2018?

1, 2, 1009, 2018

There is a total of 4 positive divisors.
The sum of these divisors is 3030.
The arithmetic mean is 757.5.

2 even divisors

2, 2018

2 odd divisors

1, 1009

How to compute the divisors of 2018?

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 2018 by each of the numbers from 1 to 2018 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)

2018 / 1 = 2018 (the remainder is 0, so 1 is a divisor of 2018)
2018 / 2 = 1009 (the remainder is 0, so 2 is a divisor of 2018)
2018 / 3 = 672.66666666667 (the remainder is 2, so 3 is not a divisor of 2018)
...
2018 / 2017 = 1.0004957858205 (the remainder is 1, so 2017 is not a divisor of 2018)
2018 / 2018 = 1 (the remainder is 0, so 2018 is a divisor of 2018)

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 2018 (i.e. 44.922154890432). 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 $\frac{N}{d} = D$ )

2018 / 1 = 2018 (the remainder is 0, so 1 and 2018 are divisors of 2018)
2018 / 2 = 1009 (the remainder is 0, so 2 and 1009 are divisors of 2018)
2018 / 3 = 672.66666666667 (the remainder is 2, so 3 is not a divisor of 2018)
...
2018 / 43 = 46.93023255814 (the remainder is 40, so 43 is not a divisor of 2018)
2018 / 44 = 45.863636363636 (the remainder is 38, so 44 is not a divisor of 2018)