What are the divisors of 8068?

1, 2, 4, 2017, 4034, 8068

There is a total of 6 positive divisors.
The sum of these divisors is 14126.
The arithmetic mean is 2354.3333333333.

4 even divisors

2, 4, 4034, 8068

2 odd divisors

1, 2017

How to compute the divisors of 8068?

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 8068 by each of the numbers from 1 to 8068 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)

8068 / 1 = 8068 (the remainder is 0, so 1 is a divisor of 8068)
8068 / 2 = 4034 (the remainder is 0, so 2 is a divisor of 8068)
8068 / 3 = 2689.3333333333 (the remainder is 1, so 3 is not a divisor of 8068)
...
8068 / 8067 = 1.0001239618198 (the remainder is 1, so 8067 is not a divisor of 8068)
8068 / 8068 = 1 (the remainder is 0, so 8068 is a divisor of 8068)

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 8068 (i.e. 89.822046291542). 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 $\frac{N}{d} = D$ )

8068 / 1 = 8068 (the remainder is 0, so 1 and 8068 are divisors of 8068)
8068 / 2 = 4034 (the remainder is 0, so 2 and 4034 are divisors of 8068)
8068 / 3 = 2689.3333333333 (the remainder is 1, so 3 is not a divisor of 8068)
...
8068 / 88 = 91.681818181818 (the remainder is 60, so 88 is not a divisor of 8068)
8068 / 89 = 90.651685393258 (the remainder is 58, so 89 is not a divisor of 8068)