What are the divisors of 1908?

1, 2, 3, 4, 6, 9, 12, 18, 36, 53, 106, 159, 212, 318, 477, 636, 954, 1908

There is a total of 18 positive divisors.
The sum of these divisors is 4914.
The arithmetic mean is 273.

12 even divisors

2, 4, 6, 12, 18, 36, 106, 212, 318, 636, 954, 1908

6 odd divisors

1, 3, 9, 53, 159, 477

How to compute the divisors of 1908?

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 1908 by each of the numbers from 1 to 1908 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)

1908 / 1 = 1908 (the remainder is 0, so 1 is a divisor of 1908)
1908 / 2 = 954 (the remainder is 0, so 2 is a divisor of 1908)
1908 / 3 = 636 (the remainder is 0, so 3 is a divisor of 1908)
...
1908 / 1907 = 1.000524383849 (the remainder is 1, so 1907 is not a divisor of 1908)
1908 / 1908 = 1 (the remainder is 0, so 1908 is a divisor of 1908)

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 1908 (i.e. 43.680659335683). 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 $\frac{N}{d} = D$ )

1908 / 1 = 1908 (the remainder is 0, so 1 and 1908 are divisors of 1908)
1908 / 2 = 954 (the remainder is 0, so 2 and 954 are divisors of 1908)
1908 / 3 = 636 (the remainder is 0, so 3 and 636 are divisors of 1908)
...
1908 / 42 = 45.428571428571 (the remainder is 18, so 42 is not a divisor of 1908)
1908 / 43 = 44.372093023256 (the remainder is 16, so 43 is not a divisor of 1908)