What are the divisors of 8184?

1, 2, 3, 4, 6, 8, 11, 12, 22, 24, 31, 33, 44, 62, 66, 88, 93, 124, 132, 186, 248, 264, 341, 372, 682, 744, 1023, 1364, 2046, 2728, 4092, 8184

There is a total of 32 positive divisors.
The sum of these divisors is 23040.
The arithmetic mean is 720.

24 even divisors

2, 4, 6, 8, 12, 22, 24, 44, 62, 66, 88, 124, 132, 186, 248, 264, 372, 682, 744, 1364, 2046, 2728, 4092, 8184

8 odd divisors

1, 3, 11, 31, 33, 93, 341, 1023

How to compute the divisors of 8184?

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 8184 by each of the numbers from 1 to 8184 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)

8184 / 1 = 8184 (the remainder is 0, so 1 is a divisor of 8184)
8184 / 2 = 4092 (the remainder is 0, so 2 is a divisor of 8184)
8184 / 3 = 2728 (the remainder is 0, so 3 is a divisor of 8184)
...
8184 / 8183 = 1.0001222045705 (the remainder is 1, so 8183 is not a divisor of 8184)
8184 / 8184 = 1 (the remainder is 0, so 8184 is a divisor of 8184)

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 8184 (i.e. 90.465463023189). 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 $\frac{N}{d} = D$ )

8184 / 1 = 8184 (the remainder is 0, so 1 and 8184 are divisors of 8184)
8184 / 2 = 4092 (the remainder is 0, so 2 and 4092 are divisors of 8184)
8184 / 3 = 2728 (the remainder is 0, so 3 and 2728 are divisors of 8184)
...
8184 / 89 = 91.955056179775 (the remainder is 85, so 89 is not a divisor of 8184)
8184 / 90 = 90.933333333333 (the remainder is 84, so 90 is not a divisor of 8184)