What are the divisors of 5908?

1, 2, 4, 7, 14, 28, 211, 422, 844, 1477, 2954, 5908

There is a total of 12 positive divisors.
The sum of these divisors is 11872.
The arithmetic mean is 989.33333333333.

8 even divisors

2, 4, 14, 28, 422, 844, 2954, 5908

4 odd divisors

1, 7, 211, 1477

How to compute the divisors of 5908?

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 5908 by each of the numbers from 1 to 5908 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)

5908 / 1 = 5908 (the remainder is 0, so 1 is a divisor of 5908)
5908 / 2 = 2954 (the remainder is 0, so 2 is a divisor of 5908)
5908 / 3 = 1969.3333333333 (the remainder is 1, so 3 is not a divisor of 5908)
...
5908 / 5907 = 1.0001692906721 (the remainder is 1, so 5907 is not a divisor of 5908)
5908 / 5908 = 1 (the remainder is 0, so 5908 is a divisor of 5908)

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 5908 (i.e. 76.863515402303). 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 $\frac{N}{d} = D$ )

5908 / 1 = 5908 (the remainder is 0, so 1 and 5908 are divisors of 5908)
5908 / 2 = 2954 (the remainder is 0, so 2 and 2954 are divisors of 5908)
5908 / 3 = 1969.3333333333 (the remainder is 1, so 3 is not a divisor of 5908)
...
5908 / 75 = 78.773333333333 (the remainder is 58, so 75 is not a divisor of 5908)
5908 / 76 = 77.736842105263 (the remainder is 56, so 76 is not a divisor of 5908)