What are the divisors of 3586?

1, 2, 11, 22, 163, 326, 1793, 3586

There is a total of 8 positive divisors.
The sum of these divisors is 5904.
The arithmetic mean is 738.

4 even divisors

2, 22, 326, 3586

4 odd divisors

1, 11, 163, 1793

How to compute the divisors of 3586?

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 3586 by each of the numbers from 1 to 3586 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)

3586 / 1 = 3586 (the remainder is 0, so 1 is a divisor of 3586)
3586 / 2 = 1793 (the remainder is 0, so 2 is a divisor of 3586)
3586 / 3 = 1195.3333333333 (the remainder is 1, so 3 is not a divisor of 3586)
...
3586 / 3585 = 1.0002789400279 (the remainder is 1, so 3585 is not a divisor of 3586)
3586 / 3586 = 1 (the remainder is 0, so 3586 is a divisor of 3586)

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 3586 (i.e. 59.883219686319). 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 $\frac{N}{d} = D$ )

3586 / 1 = 3586 (the remainder is 0, so 1 and 3586 are divisors of 3586)
3586 / 2 = 1793 (the remainder is 0, so 2 and 1793 are divisors of 3586)
3586 / 3 = 1195.3333333333 (the remainder is 1, so 3 is not a divisor of 3586)
...
3586 / 58 = 61.827586206897 (the remainder is 48, so 58 is not a divisor of 3586)
3586 / 59 = 60.779661016949 (the remainder is 46, so 59 is not a divisor of 3586)