What are the divisors of 2568?

1, 2, 3, 4, 6, 8, 12, 24, 107, 214, 321, 428, 642, 856, 1284, 2568

There is a total of 16 positive divisors.
The sum of these divisors is 6480.
The arithmetic mean is 405.

12 even divisors

2, 4, 6, 8, 12, 24, 214, 428, 642, 856, 1284, 2568

4 odd divisors

1, 3, 107, 321

How to compute the divisors of 2568?

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 2568 by each of the numbers from 1 to 2568 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)

2568 / 1 = 2568 (the remainder is 0, so 1 is a divisor of 2568)
2568 / 2 = 1284 (the remainder is 0, so 2 is a divisor of 2568)
2568 / 3 = 856 (the remainder is 0, so 3 is a divisor of 2568)
...
2568 / 2567 = 1.0003895597974 (the remainder is 1, so 2567 is not a divisor of 2568)
2568 / 2568 = 1 (the remainder is 0, so 2568 is a divisor of 2568)

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 2568 (i.e. 50.67543783728). 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 $\frac{N}{d} = D$ )

2568 / 1 = 2568 (the remainder is 0, so 1 and 2568 are divisors of 2568)
2568 / 2 = 1284 (the remainder is 0, so 2 and 1284 are divisors of 2568)
2568 / 3 = 856 (the remainder is 0, so 3 and 856 are divisors of 2568)
...
2568 / 49 = 52.408163265306 (the remainder is 20, so 49 is not a divisor of 2568)
2568 / 50 = 51.36 (the remainder is 18, so 50 is not a divisor of 2568)