What are the divisors of 8256?

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 43, 48, 64, 86, 96, 129, 172, 192, 258, 344, 516, 688, 1032, 1376, 2064, 2752, 4128, 8256

There is a total of 28 positive divisors.
The sum of these divisors is 22352.
The arithmetic mean is 798.28571428571.

24 even divisors

2, 4, 6, 8, 12, 16, 24, 32, 48, 64, 86, 96, 172, 192, 258, 344, 516, 688, 1032, 1376, 2064, 2752, 4128, 8256

4 odd divisors

1, 3, 43, 129

How to compute the divisors of 8256?

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 8256 by each of the numbers from 1 to 8256 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)

8256 / 1 = 8256 (the remainder is 0, so 1 is a divisor of 8256)
8256 / 2 = 4128 (the remainder is 0, so 2 is a divisor of 8256)
8256 / 3 = 2752 (the remainder is 0, so 3 is a divisor of 8256)
...
8256 / 8255 = 1.0001211387038 (the remainder is 1, so 8255 is not a divisor of 8256)
8256 / 8256 = 1 (the remainder is 0, so 8256 is a divisor of 8256)

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 8256 (i.e. 90.862533532804). 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 $\frac{N}{d} = D$ )

8256 / 1 = 8256 (the remainder is 0, so 1 and 8256 are divisors of 8256)
8256 / 2 = 4128 (the remainder is 0, so 2 and 4128 are divisors of 8256)
8256 / 3 = 2752 (the remainder is 0, so 3 and 2752 are divisors of 8256)
...
8256 / 89 = 92.76404494382 (the remainder is 68, so 89 is not a divisor of 8256)
8256 / 90 = 91.733333333333 (the remainder is 66, so 90 is not a divisor of 8256)