What are the divisors of 8302?

1, 2, 7, 14, 593, 1186, 4151, 8302

There is a total of 8 positive divisors.
The sum of these divisors is 14256.
The arithmetic mean is 1782.

4 even divisors

2, 14, 1186, 8302

4 odd divisors

1, 7, 593, 4151

How to compute the divisors of 8302?

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 8302 by each of the numbers from 1 to 8302 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)

8302 / 1 = 8302 (the remainder is 0, so 1 is a divisor of 8302)
8302 / 2 = 4151 (the remainder is 0, so 2 is a divisor of 8302)
8302 / 3 = 2767.3333333333 (the remainder is 1, so 3 is not a divisor of 8302)
...
8302 / 8301 = 1.0001204674136 (the remainder is 1, so 8301 is not a divisor of 8302)
8302 / 8302 = 1 (the remainder is 0, so 8302 is a divisor of 8302)

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 8302 (i.e. 91.115311556291). 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 $\frac{N}{d} = D$ )

8302 / 1 = 8302 (the remainder is 0, so 1 and 8302 are divisors of 8302)
8302 / 2 = 4151 (the remainder is 0, so 2 and 4151 are divisors of 8302)
8302 / 3 = 2767.3333333333 (the remainder is 1, so 3 is not a divisor of 8302)
...
8302 / 90 = 92.244444444444 (the remainder is 22, so 90 is not a divisor of 8302)
8302 / 91 = 91.230769230769 (the remainder is 21, so 91 is not a divisor of 8302)