What are the divisors of 8067?

1, 3, 2689, 8067

There is a total of 4 positive divisors.
The sum of these divisors is 10760.
The arithmetic mean is 2690.

4 odd divisors

1, 3, 2689, 8067

How to compute the divisors of 8067?

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 8067 by each of the numbers from 1 to 8067 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)

8067 / 1 = 8067 (the remainder is 0, so 1 is a divisor of 8067)
8067 / 2 = 4033.5 (the remainder is 1, so 2 is not a divisor of 8067)
8067 / 3 = 2689 (the remainder is 0, so 3 is a divisor of 8067)
...
8067 / 8066 = 1.0001239771882 (the remainder is 1, so 8066 is not a divisor of 8067)
8067 / 8067 = 1 (the remainder is 0, so 8067 is a divisor of 8067)

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 8067 (i.e. 89.816479556928). 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 $\frac{N}{d} = D$ )

8067 / 1 = 8067 (the remainder is 0, so 1 and 8067 are divisors of 8067)
8067 / 2 = 4033.5 (the remainder is 1, so 2 is not a divisor of 8067)
8067 / 3 = 2689 (the remainder is 0, so 3 and 2689 are divisors of 8067)
...
8067 / 88 = 91.670454545455 (the remainder is 59, so 88 is not a divisor of 8067)
8067 / 89 = 90.640449438202 (the remainder is 57, so 89 is not a divisor of 8067)