What are the divisors of 8108?

1, 2, 4, 2027, 4054, 8108

There is a total of 6 positive divisors.
The sum of these divisors is 14196.
The arithmetic mean is 2366.

4 even divisors

2, 4, 4054, 8108

2 odd divisors

1, 2027

How to compute the divisors of 8108?

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 8108 by each of the numbers from 1 to 8108 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)

8108 / 1 = 8108 (the remainder is 0, so 1 is a divisor of 8108)
8108 / 2 = 4054 (the remainder is 0, so 2 is a divisor of 8108)
8108 / 3 = 2702.6666666667 (the remainder is 2, so 3 is not a divisor of 8108)
...
8108 / 8107 = 1.0001233501912 (the remainder is 1, so 8107 is not a divisor of 8108)
8108 / 8108 = 1 (the remainder is 0, so 8108 is a divisor of 8108)

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 8108 (i.e. 90.044433475923). 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 $\frac{N}{d} = D$ )

8108 / 1 = 8108 (the remainder is 0, so 1 and 8108 are divisors of 8108)
8108 / 2 = 4054 (the remainder is 0, so 2 and 4054 are divisors of 8108)
8108 / 3 = 2702.6666666667 (the remainder is 2, so 3 is not a divisor of 8108)
...
8108 / 89 = 91.101123595506 (the remainder is 9, so 89 is not a divisor of 8108)
8108 / 90 = 90.088888888889 (the remainder is 8, so 90 is not a divisor of 8108)