What are the divisors of 4108?

1, 2, 4, 13, 26, 52, 79, 158, 316, 1027, 2054, 4108

There is a total of 12 positive divisors.
The sum of these divisors is 7840.
The arithmetic mean is 653.33333333333.

8 even divisors

2, 4, 26, 52, 158, 316, 2054, 4108

4 odd divisors

1, 13, 79, 1027

How to compute the divisors of 4108?

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 4108 by each of the numbers from 1 to 4108 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)

4108 / 1 = 4108 (the remainder is 0, so 1 is a divisor of 4108)
4108 / 2 = 2054 (the remainder is 0, so 2 is a divisor of 4108)
4108 / 3 = 1369.3333333333 (the remainder is 1, so 3 is not a divisor of 4108)
...
4108 / 4107 = 1.00024348673 (the remainder is 1, so 4107 is not a divisor of 4108)
4108 / 4108 = 1 (the remainder is 0, so 4108 is a divisor of 4108)

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 4108 (i.e. 64.093681435848). 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 $\frac{N}{d} = D$ )

4108 / 1 = 4108 (the remainder is 0, so 1 and 4108 are divisors of 4108)
4108 / 2 = 2054 (the remainder is 0, so 2 and 2054 are divisors of 4108)
4108 / 3 = 1369.3333333333 (the remainder is 1, so 3 is not a divisor of 4108)
...
4108 / 63 = 65.206349206349 (the remainder is 13, so 63 is not a divisor of 4108)
4108 / 64 = 64.1875 (the remainder is 12, so 64 is not a divisor of 4108)