What are the divisors of 569?

1, 569

There is a total of 2 positive divisors.
The sum of these divisors is 570.
The arithmetic mean is 285.

2 odd divisors

1, 569

How to compute the divisors of 569?

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 569 by each of the numbers from 1 to 569 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)

569 / 1 = 569 (the remainder is 0, so 1 is a divisor of 569)
569 / 2 = 284.5 (the remainder is 1, so 2 is not a divisor of 569)
569 / 3 = 189.66666666667 (the remainder is 2, so 3 is not a divisor of 569)
...
569 / 568 = 1.0017605633803 (the remainder is 1, so 568 is not a divisor of 569)
569 / 569 = 1 (the remainder is 0, so 569 is a divisor of 569)

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 569 (i.e. 23.853720883753). 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 $\frac{N}{d} = D$ )

569 / 1 = 569 (the remainder is 0, so 1 and 569 are divisors of 569)
569 / 2 = 284.5 (the remainder is 1, so 2 is not a divisor of 569)
569 / 3 = 189.66666666667 (the remainder is 2, so 3 is not a divisor of 569)
...
569 / 22 = 25.863636363636 (the remainder is 19, so 22 is not a divisor of 569)
569 / 23 = 24.739130434783 (the remainder is 17, so 23 is not a divisor of 569)