What are the divisors of 568?

1, 2, 4, 8, 71, 142, 284, 568

There is a total of 8 positive divisors.
The sum of these divisors is 1080.
The arithmetic mean is 135.

6 even divisors

2, 4, 8, 142, 284, 568

2 odd divisors

1, 71

How to compute the divisors of 568?

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 568 by each of the numbers from 1 to 568 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)

568 / 1 = 568 (the remainder is 0, so 1 is a divisor of 568)
568 / 2 = 284 (the remainder is 0, so 2 is a divisor of 568)
568 / 3 = 189.33333333333 (the remainder is 1, so 3 is not a divisor of 568)
...
568 / 567 = 1.0017636684303 (the remainder is 1, so 567 is not a divisor of 568)
568 / 568 = 1 (the remainder is 0, so 568 is a divisor of 568)

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 568 (i.e. 23.832750575626). 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 $\frac{N}{d} = D$ )

568 / 1 = 568 (the remainder is 0, so 1 and 568 are divisors of 568)
568 / 2 = 284 (the remainder is 0, so 2 and 284 are divisors of 568)
568 / 3 = 189.33333333333 (the remainder is 1, so 3 is not a divisor of 568)
...
568 / 22 = 25.818181818182 (the remainder is 18, so 22 is not a divisor of 568)
568 / 23 = 24.695652173913 (the remainder is 16, so 23 is not a divisor of 568)