What are the divisors of 9018?

1, 2, 3, 6, 9, 18, 27, 54, 167, 334, 501, 1002, 1503, 3006, 4509, 9018

There is a total of 16 positive divisors.
The sum of these divisors is 20160.
The arithmetic mean is 1260.

8 even divisors

2, 6, 18, 54, 334, 1002, 3006, 9018

8 odd divisors

1, 3, 9, 27, 167, 501, 1503, 4509

How to compute the divisors of 9018?

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 9018 by each of the numbers from 1 to 9018 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)

9018 / 1 = 9018 (the remainder is 0, so 1 is a divisor of 9018)
9018 / 2 = 4509 (the remainder is 0, so 2 is a divisor of 9018)
9018 / 3 = 3006 (the remainder is 0, so 3 is a divisor of 9018)
...
9018 / 9017 = 1.0001109016303 (the remainder is 1, so 9017 is not a divisor of 9018)
9018 / 9018 = 1 (the remainder is 0, so 9018 is a divisor of 9018)

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 9018 (i.e. 94.963150748066). 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 $\frac{N}{d} = D$ )

9018 / 1 = 9018 (the remainder is 0, so 1 and 9018 are divisors of 9018)
9018 / 2 = 4509 (the remainder is 0, so 2 and 4509 are divisors of 9018)
9018 / 3 = 3006 (the remainder is 0, so 3 and 3006 are divisors of 9018)
...
9018 / 93 = 96.967741935484 (the remainder is 90, so 93 is not a divisor of 9018)
9018 / 94 = 95.936170212766 (the remainder is 88, so 94 is not a divisor of 9018)