What are the divisors of 8308?

1, 2, 4, 31, 62, 67, 124, 134, 268, 2077, 4154, 8308

There is a total of 12 positive divisors.
The sum of these divisors is 15232.
The arithmetic mean is 1269.3333333333.

8 even divisors

2, 4, 62, 124, 134, 268, 4154, 8308

4 odd divisors

1, 31, 67, 2077

How to compute the divisors of 8308?

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 8308 by each of the numbers from 1 to 8308 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)

8308 / 1 = 8308 (the remainder is 0, so 1 is a divisor of 8308)
8308 / 2 = 4154 (the remainder is 0, so 2 is a divisor of 8308)
8308 / 3 = 2769.3333333333 (the remainder is 1, so 3 is not a divisor of 8308)
...
8308 / 8307 = 1.0001203804021 (the remainder is 1, so 8307 is not a divisor of 8308)
8308 / 8308 = 1 (the remainder is 0, so 8308 is a divisor of 8308)

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 8308 (i.e. 91.148230920847). 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 $\frac{N}{d} = D$ )

8308 / 1 = 8308 (the remainder is 0, so 1 and 8308 are divisors of 8308)
8308 / 2 = 4154 (the remainder is 0, so 2 and 4154 are divisors of 8308)
8308 / 3 = 2769.3333333333 (the remainder is 1, so 3 is not a divisor of 8308)
...
8308 / 90 = 92.311111111111 (the remainder is 28, so 90 is not a divisor of 8308)
8308 / 91 = 91.296703296703 (the remainder is 27, so 91 is not a divisor of 8308)