What are the divisors of 8208?

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 19, 24, 27, 36, 38, 48, 54, 57, 72, 76, 108, 114, 144, 152, 171, 216, 228, 304, 342, 432, 456, 513, 684, 912, 1026, 1368, 2052, 2736, 4104, 8208

There is a total of 40 positive divisors.
The sum of these divisors is 24800.
The arithmetic mean is 620.

32 even divisors

2, 4, 6, 8, 12, 16, 18, 24, 36, 38, 48, 54, 72, 76, 108, 114, 144, 152, 216, 228, 304, 342, 432, 456, 684, 912, 1026, 1368, 2052, 2736, 4104, 8208

8 odd divisors

1, 3, 9, 19, 27, 57, 171, 513

How to compute the divisors of 8208?

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 8208 by each of the numbers from 1 to 8208 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)

8208 / 1 = 8208 (the remainder is 0, so 1 is a divisor of 8208)
8208 / 2 = 4104 (the remainder is 0, so 2 is a divisor of 8208)
8208 / 3 = 2736 (the remainder is 0, so 3 is a divisor of 8208)
...
8208 / 8207 = 1.0001218472036 (the remainder is 1, so 8207 is not a divisor of 8208)
8208 / 8208 = 1 (the remainder is 0, so 8208 is a divisor of 8208)

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 8208 (i.e. 90.598013223249). 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 $\frac{N}{d} = D$ )

8208 / 1 = 8208 (the remainder is 0, so 1 and 8208 are divisors of 8208)
8208 / 2 = 4104 (the remainder is 0, so 2 and 4104 are divisors of 8208)
8208 / 3 = 2736 (the remainder is 0, so 3 and 2736 are divisors of 8208)
...
8208 / 89 = 92.224719101124 (the remainder is 20, so 89 is not a divisor of 8208)
8208 / 90 = 91.2 (the remainder is 18, so 90 is not a divisor of 8208)