What are the divisors of 8094?

1, 2, 3, 6, 19, 38, 57, 71, 114, 142, 213, 426, 1349, 2698, 4047, 8094

There is a total of 16 positive divisors.
The sum of these divisors is 17280.
The arithmetic mean is 1080.

8 even divisors

2, 6, 38, 114, 142, 426, 2698, 8094

8 odd divisors

1, 3, 19, 57, 71, 213, 1349, 4047

How to compute the divisors of 8094?

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 8094 by each of the numbers from 1 to 8094 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)

8094 / 1 = 8094 (the remainder is 0, so 1 is a divisor of 8094)
8094 / 2 = 4047 (the remainder is 0, so 2 is a divisor of 8094)
8094 / 3 = 2698 (the remainder is 0, so 3 is a divisor of 8094)
...
8094 / 8093 = 1.0001235635735 (the remainder is 1, so 8093 is not a divisor of 8094)
8094 / 8094 = 1 (the remainder is 0, so 8094 is a divisor of 8094)

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 8094 (i.e. 89.96666049154). 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 $\frac{N}{d} = D$ )

8094 / 1 = 8094 (the remainder is 0, so 1 and 8094 are divisors of 8094)
8094 / 2 = 4047 (the remainder is 0, so 2 and 4047 are divisors of 8094)
8094 / 3 = 2698 (the remainder is 0, so 3 and 2698 are divisors of 8094)
...
8094 / 88 = 91.977272727273 (the remainder is 86, so 88 is not a divisor of 8094)
8094 / 89 = 90.943820224719 (the remainder is 84, so 89 is not a divisor of 8094)