What are the divisors of 558?

1, 2, 3, 6, 9, 18, 31, 62, 93, 186, 279, 558

There is a total of 12 positive divisors.
The sum of these divisors is 1248.
The arithmetic mean is 104.

6 even divisors

2, 6, 18, 62, 186, 558

6 odd divisors

1, 3, 9, 31, 93, 279

How to compute the divisors of 558?

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 558 by each of the numbers from 1 to 558 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)

558 / 1 = 558 (the remainder is 0, so 1 is a divisor of 558)
558 / 2 = 279 (the remainder is 0, so 2 is a divisor of 558)
558 / 3 = 186 (the remainder is 0, so 3 is a divisor of 558)
...
558 / 557 = 1.0017953321364 (the remainder is 1, so 557 is not a divisor of 558)
558 / 558 = 1 (the remainder is 0, so 558 is a divisor of 558)

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 558 (i.e. 23.622023622035). 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 $\frac{N}{d} = D$ )

558 / 1 = 558 (the remainder is 0, so 1 and 558 are divisors of 558)
558 / 2 = 279 (the remainder is 0, so 2 and 279 are divisors of 558)
558 / 3 = 186 (the remainder is 0, so 3 and 186 are divisors of 558)
...
558 / 22 = 25.363636363636 (the remainder is 8, so 22 is not a divisor of 558)
558 / 23 = 24.260869565217 (the remainder is 6, so 23 is not a divisor of 558)