What are the divisors of 8018?

1, 2, 19, 38, 211, 422, 4009, 8018

There is a total of 8 positive divisors.
The sum of these divisors is 12720.
The arithmetic mean is 1590.

4 even divisors

2, 38, 422, 8018

4 odd divisors

1, 19, 211, 4009

How to compute the divisors of 8018?

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 8018 by each of the numbers from 1 to 8018 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)

8018 / 1 = 8018 (the remainder is 0, so 1 is a divisor of 8018)
8018 / 2 = 4009 (the remainder is 0, so 2 is a divisor of 8018)
8018 / 3 = 2672.6666666667 (the remainder is 2, so 3 is not a divisor of 8018)
...
8018 / 8017 = 1.0001247349383 (the remainder is 1, so 8017 is not a divisor of 8018)
8018 / 8018 = 1 (the remainder is 0, so 8018 is a divisor of 8018)

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 8018 (i.e. 89.543285622095). 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 $\frac{N}{d} = D$ )

8018 / 1 = 8018 (the remainder is 0, so 1 and 8018 are divisors of 8018)
8018 / 2 = 4009 (the remainder is 0, so 2 and 4009 are divisors of 8018)
8018 / 3 = 2672.6666666667 (the remainder is 2, so 3 is not a divisor of 8018)
...
8018 / 88 = 91.113636363636 (the remainder is 10, so 88 is not a divisor of 8018)
8018 / 89 = 90.089887640449 (the remainder is 8, so 89 is not a divisor of 8018)