What are the divisors of 8266?

1, 2, 4133, 8266

There is a total of 4 positive divisors.
The sum of these divisors is 12402.
The arithmetic mean is 3100.5.

2 even divisors

2, 8266

2 odd divisors

1, 4133

How to compute the divisors of 8266?

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 8266 by each of the numbers from 1 to 8266 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)

8266 / 1 = 8266 (the remainder is 0, so 1 is a divisor of 8266)
8266 / 2 = 4133 (the remainder is 0, so 2 is a divisor of 8266)
8266 / 3 = 2755.3333333333 (the remainder is 1, so 3 is not a divisor of 8266)
...
8266 / 8265 = 1.0001209921355 (the remainder is 1, so 8265 is not a divisor of 8266)
8266 / 8266 = 1 (the remainder is 0, so 8266 is a divisor of 8266)

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 8266 (i.e. 90.917545061446). 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 $\frac{N}{d} = D$ )

8266 / 1 = 8266 (the remainder is 0, so 1 and 8266 are divisors of 8266)
8266 / 2 = 4133 (the remainder is 0, so 2 and 4133 are divisors of 8266)
8266 / 3 = 2755.3333333333 (the remainder is 1, so 3 is not a divisor of 8266)
...
8266 / 89 = 92.876404494382 (the remainder is 78, so 89 is not a divisor of 8266)
8266 / 90 = 91.844444444444 (the remainder is 76, so 90 is not a divisor of 8266)