What are the divisors of 8204?

1, 2, 4, 7, 14, 28, 293, 586, 1172, 2051, 4102, 8204

There is a total of 12 positive divisors.
The sum of these divisors is 16464.
The arithmetic mean is 1372.

8 even divisors

2, 4, 14, 28, 586, 1172, 4102, 8204

4 odd divisors

1, 7, 293, 2051

How to compute the divisors of 8204?

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 8204 by each of the numbers from 1 to 8204 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)

8204 / 1 = 8204 (the remainder is 0, so 1 is a divisor of 8204)
8204 / 2 = 4102 (the remainder is 0, so 2 is a divisor of 8204)
8204 / 3 = 2734.6666666667 (the remainder is 2, so 3 is not a divisor of 8204)
...
8204 / 8203 = 1.0001219066195 (the remainder is 1, so 8203 is not a divisor of 8204)
8204 / 8204 = 1 (the remainder is 0, so 8204 is a divisor of 8204)

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 8204 (i.e. 90.575934993794). 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 $\frac{N}{d} = D$ )

8204 / 1 = 8204 (the remainder is 0, so 1 and 8204 are divisors of 8204)
8204 / 2 = 4102 (the remainder is 0, so 2 and 4102 are divisors of 8204)
8204 / 3 = 2734.6666666667 (the remainder is 2, so 3 is not a divisor of 8204)
...
8204 / 89 = 92.179775280899 (the remainder is 16, so 89 is not a divisor of 8204)
8204 / 90 = 91.155555555556 (the remainder is 14, so 90 is not a divisor of 8204)