What are the divisors of 6108?

1, 2, 3, 4, 6, 12, 509, 1018, 1527, 2036, 3054, 6108

There is a total of 12 positive divisors.
The sum of these divisors is 14280.
The arithmetic mean is 1190.

8 even divisors

2, 4, 6, 12, 1018, 2036, 3054, 6108

4 odd divisors

1, 3, 509, 1527

How to compute the divisors of 6108?

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 6108 by each of the numbers from 1 to 6108 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)

6108 / 1 = 6108 (the remainder is 0, so 1 is a divisor of 6108)
6108 / 2 = 3054 (the remainder is 0, so 2 is a divisor of 6108)
6108 / 3 = 2036 (the remainder is 0, so 3 is a divisor of 6108)
...
6108 / 6107 = 1.0001637465204 (the remainder is 1, so 6107 is not a divisor of 6108)
6108 / 6108 = 1 (the remainder is 0, so 6108 is a divisor of 6108)

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 6108 (i.e. 78.15369473032). 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 $\frac{N}{d} = D$ )

6108 / 1 = 6108 (the remainder is 0, so 1 and 6108 are divisors of 6108)
6108 / 2 = 3054 (the remainder is 0, so 2 and 3054 are divisors of 6108)
6108 / 3 = 2036 (the remainder is 0, so 3 and 2036 are divisors of 6108)
...
6108 / 77 = 79.324675324675 (the remainder is 25, so 77 is not a divisor of 6108)
6108 / 78 = 78.307692307692 (the remainder is 24, so 78 is not a divisor of 6108)