What are the divisors of 4568?

1, 2, 4, 8, 571, 1142, 2284, 4568

There is a total of 8 positive divisors.
The sum of these divisors is 8580.
The arithmetic mean is 1072.5.

6 even divisors

2, 4, 8, 1142, 2284, 4568

2 odd divisors

1, 571

How to compute the divisors of 4568?

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 4568 by each of the numbers from 1 to 4568 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)

4568 / 1 = 4568 (the remainder is 0, so 1 is a divisor of 4568)
4568 / 2 = 2284 (the remainder is 0, so 2 is a divisor of 4568)
4568 / 3 = 1522.6666666667 (the remainder is 2, so 3 is not a divisor of 4568)
...
4568 / 4567 = 1.0002189621196 (the remainder is 1, so 4567 is not a divisor of 4568)
4568 / 4568 = 1 (the remainder is 0, so 4568 is a divisor of 4568)

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 4568 (i.e. 67.586980994863). 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 $\frac{N}{d} = D$ )

4568 / 1 = 4568 (the remainder is 0, so 1 and 4568 are divisors of 4568)
4568 / 2 = 2284 (the remainder is 0, so 2 and 2284 are divisors of 4568)
4568 / 3 = 1522.6666666667 (the remainder is 2, so 3 is not a divisor of 4568)
...
4568 / 66 = 69.212121212121 (the remainder is 14, so 66 is not a divisor of 4568)
4568 / 67 = 68.179104477612 (the remainder is 12, so 67 is not a divisor of 4568)