What are the divisors of 2808?

1, 2, 3, 4, 6, 8, 9, 12, 13, 18, 24, 26, 27, 36, 39, 52, 54, 72, 78, 104, 108, 117, 156, 216, 234, 312, 351, 468, 702, 936, 1404, 2808

There is a total of 32 positive divisors.
The sum of these divisors is 8400.
The arithmetic mean is 262.5.

24 even divisors

2, 4, 6, 8, 12, 18, 24, 26, 36, 52, 54, 72, 78, 104, 108, 156, 216, 234, 312, 468, 702, 936, 1404, 2808

8 odd divisors

1, 3, 9, 13, 27, 39, 117, 351

How to compute the divisors of 2808?

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 2808 by each of the numbers from 1 to 2808 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)

2808 / 1 = 2808 (the remainder is 0, so 1 is a divisor of 2808)
2808 / 2 = 1404 (the remainder is 0, so 2 is a divisor of 2808)
2808 / 3 = 936 (the remainder is 0, so 3 is a divisor of 2808)
...
2808 / 2807 = 1.0003562522266 (the remainder is 1, so 2807 is not a divisor of 2808)
2808 / 2808 = 1 (the remainder is 0, so 2808 is a divisor of 2808)

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 2808 (i.e. 52.990565197967). 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 $\frac{N}{d} = D$ )

2808 / 1 = 2808 (the remainder is 0, so 1 and 2808 are divisors of 2808)
2808 / 2 = 1404 (the remainder is 0, so 2 and 1404 are divisors of 2808)
2808 / 3 = 936 (the remainder is 0, so 3 and 936 are divisors of 2808)
...
2808 / 51 = 55.058823529412 (the remainder is 3, so 51 is not a divisor of 2808)
2808 / 52 = 54 (the remainder is 0, so 52 and 54 are divisors of 2808)