What are the divisors of 8096?

1, 2, 4, 8, 11, 16, 22, 23, 32, 44, 46, 88, 92, 176, 184, 253, 352, 368, 506, 736, 1012, 2024, 4048, 8096

There is a total of 24 positive divisors.
The sum of these divisors is 18144.
The arithmetic mean is 756.

20 even divisors

2, 4, 8, 16, 22, 32, 44, 46, 88, 92, 176, 184, 352, 368, 506, 736, 1012, 2024, 4048, 8096

4 odd divisors

1, 11, 23, 253

How to compute the divisors of 8096?

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 8096 by each of the numbers from 1 to 8096 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)

8096 / 1 = 8096 (the remainder is 0, so 1 is a divisor of 8096)
8096 / 2 = 4048 (the remainder is 0, so 2 is a divisor of 8096)
8096 / 3 = 2698.6666666667 (the remainder is 2, so 3 is not a divisor of 8096)
...
8096 / 8095 = 1.0001235330451 (the remainder is 1, so 8095 is not a divisor of 8096)
8096 / 8096 = 1 (the remainder is 0, so 8096 is a divisor of 8096)

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 8096 (i.e. 89.977775033616). 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 $\frac{N}{d} = D$ )

8096 / 1 = 8096 (the remainder is 0, so 1 and 8096 are divisors of 8096)
8096 / 2 = 4048 (the remainder is 0, so 2 and 4048 are divisors of 8096)
8096 / 3 = 2698.6666666667 (the remainder is 2, so 3 is not a divisor of 8096)
...
8096 / 88 = 92 (the remainder is 0, so 88 and 92 are divisors of 8096)
8096 / 89 = 90.966292134831 (the remainder is 86, so 89 is not a divisor of 8096)