What are the divisors of 559?

1, 13, 43, 559

There is a total of 4 positive divisors.
The sum of these divisors is 616.
The arithmetic mean is 154.

4 odd divisors

1, 13, 43, 559

How to compute the divisors of 559?

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 559 by each of the numbers from 1 to 559 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)

559 / 1 = 559 (the remainder is 0, so 1 is a divisor of 559)
559 / 2 = 279.5 (the remainder is 1, so 2 is not a divisor of 559)
559 / 3 = 186.33333333333 (the remainder is 1, so 3 is not a divisor of 559)
...
559 / 558 = 1.0017921146953 (the remainder is 1, so 558 is not a divisor of 559)
559 / 559 = 1 (the remainder is 0, so 559 is a divisor of 559)

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 559 (i.e. 23.643180835074). 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 $\frac{N}{d} = D$ )

559 / 1 = 559 (the remainder is 0, so 1 and 559 are divisors of 559)
559 / 2 = 279.5 (the remainder is 1, so 2 is not a divisor of 559)
559 / 3 = 186.33333333333 (the remainder is 1, so 3 is not a divisor of 559)
...
559 / 22 = 25.409090909091 (the remainder is 9, so 22 is not a divisor of 559)
559 / 23 = 24.304347826087 (the remainder is 7, so 23 is not a divisor of 559)