What are the divisors of 3558?

1, 2, 3, 6, 593, 1186, 1779, 3558

There is a total of 8 positive divisors.
The sum of these divisors is 7128.
The arithmetic mean is 891.

4 even divisors

2, 6, 1186, 3558

4 odd divisors

1, 3, 593, 1779

How to compute the divisors of 3558?

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 3558 by each of the numbers from 1 to 3558 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)

3558 / 1 = 3558 (the remainder is 0, so 1 is a divisor of 3558)
3558 / 2 = 1779 (the remainder is 0, so 2 is a divisor of 3558)
3558 / 3 = 1186 (the remainder is 0, so 3 is a divisor of 3558)
...
3558 / 3557 = 1.0002811357886 (the remainder is 1, so 3557 is not a divisor of 3558)
3558 / 3558 = 1 (the remainder is 0, so 3558 is a divisor of 3558)

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 3558 (i.e. 59.648973168027). 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 $\frac{N}{d} = D$ )

3558 / 1 = 3558 (the remainder is 0, so 1 and 3558 are divisors of 3558)
3558 / 2 = 1779 (the remainder is 0, so 2 and 1779 are divisors of 3558)
3558 / 3 = 1186 (the remainder is 0, so 3 and 1186 are divisors of 3558)
...
3558 / 58 = 61.344827586207 (the remainder is 20, so 58 is not a divisor of 3558)
3558 / 59 = 60.305084745763 (the remainder is 18, so 59 is not a divisor of 3558)