What are the divisors of 8306?

1, 2, 4153, 8306

There is a total of 4 positive divisors.
The sum of these divisors is 12462.
The arithmetic mean is 3115.5.

2 even divisors

2, 8306

2 odd divisors

1, 4153

How to compute the divisors of 8306?

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 8306 by each of the numbers from 1 to 8306 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)

8306 / 1 = 8306 (the remainder is 0, so 1 is a divisor of 8306)
8306 / 2 = 4153 (the remainder is 0, so 2 is a divisor of 8306)
8306 / 3 = 2768.6666666667 (the remainder is 2, so 3 is not a divisor of 8306)
...
8306 / 8305 = 1.0001204093919 (the remainder is 1, so 8305 is not a divisor of 8306)
8306 / 8306 = 1 (the remainder is 0, so 8306 is a divisor of 8306)

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 8306 (i.e. 91.137259120516). 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 $\frac{N}{d} = D$ )

8306 / 1 = 8306 (the remainder is 0, so 1 and 8306 are divisors of 8306)
8306 / 2 = 4153 (the remainder is 0, so 2 and 4153 are divisors of 8306)
8306 / 3 = 2768.6666666667 (the remainder is 2, so 3 is not a divisor of 8306)
...
8306 / 90 = 92.288888888889 (the remainder is 26, so 90 is not a divisor of 8306)
8306 / 91 = 91.274725274725 (the remainder is 25, so 91 is not a divisor of 8306)