What are the divisors of 8066?

1, 2, 37, 74, 109, 218, 4033, 8066

There is a total of 8 positive divisors.
The sum of these divisors is 12540.
The arithmetic mean is 1567.5.

4 even divisors

2, 74, 218, 8066

4 odd divisors

1, 37, 109, 4033

How to compute the divisors of 8066?

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 8066 by each of the numbers from 1 to 8066 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)

8066 / 1 = 8066 (the remainder is 0, so 1 is a divisor of 8066)
8066 / 2 = 4033 (the remainder is 0, so 2 is a divisor of 8066)
8066 / 3 = 2688.6666666667 (the remainder is 2, so 3 is not a divisor of 8066)
...
8066 / 8065 = 1.0001239925604 (the remainder is 1, so 8065 is not a divisor of 8066)
8066 / 8066 = 1 (the remainder is 0, so 8066 is a divisor of 8066)

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 8066 (i.e. 89.810912477271). 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 $\frac{N}{d} = D$ )

8066 / 1 = 8066 (the remainder is 0, so 1 and 8066 are divisors of 8066)
8066 / 2 = 4033 (the remainder is 0, so 2 and 4033 are divisors of 8066)
8066 / 3 = 2688.6666666667 (the remainder is 2, so 3 is not a divisor of 8066)
...
8066 / 88 = 91.659090909091 (the remainder is 58, so 88 is not a divisor of 8066)
8066 / 89 = 90.629213483146 (the remainder is 56, so 89 is not a divisor of 8066)