What are the divisors of 8304?

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 173, 346, 519, 692, 1038, 1384, 2076, 2768, 4152, 8304

There is a total of 20 positive divisors.
The sum of these divisors is 21576.
The arithmetic mean is 1078.8.

16 even divisors

2, 4, 6, 8, 12, 16, 24, 48, 346, 692, 1038, 1384, 2076, 2768, 4152, 8304

4 odd divisors

1, 3, 173, 519

How to compute the divisors of 8304?

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 8304 by each of the numbers from 1 to 8304 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)

8304 / 1 = 8304 (the remainder is 0, so 1 is a divisor of 8304)
8304 / 2 = 4152 (the remainder is 0, so 2 is a divisor of 8304)
8304 / 3 = 2768 (the remainder is 0, so 3 is a divisor of 8304)
...
8304 / 8303 = 1.0001204383958 (the remainder is 1, so 8303 is not a divisor of 8304)
8304 / 8304 = 1 (the remainder is 0, so 8304 is a divisor of 8304)

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 8304 (i.e. 91.126285999156). 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 $\frac{N}{d} = D$ )

8304 / 1 = 8304 (the remainder is 0, so 1 and 8304 are divisors of 8304)
8304 / 2 = 4152 (the remainder is 0, so 2 and 4152 are divisors of 8304)
8304 / 3 = 2768 (the remainder is 0, so 3 and 2768 are divisors of 8304)
...
8304 / 90 = 92.266666666667 (the remainder is 24, so 90 is not a divisor of 8304)
8304 / 91 = 91.252747252747 (the remainder is 23, so 91 is not a divisor of 8304)