What are the divisors of 586?

1, 2, 293, 586

There is a total of 4 positive divisors.
The sum of these divisors is 882.
The arithmetic mean is 220.5.

2 even divisors

2, 586

2 odd divisors

1, 293

How to compute the divisors of 586?

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 586 by each of the numbers from 1 to 586 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)

586 / 1 = 586 (the remainder is 0, so 1 is a divisor of 586)
586 / 2 = 293 (the remainder is 0, so 2 is a divisor of 586)
586 / 3 = 195.33333333333 (the remainder is 1, so 3 is not a divisor of 586)
...
586 / 585 = 1.0017094017094 (the remainder is 1, so 585 is not a divisor of 586)
586 / 586 = 1 (the remainder is 0, so 586 is a divisor of 586)

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 586 (i.e. 24.20743687382). 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 $\frac{N}{d} = D$ )

586 / 1 = 586 (the remainder is 0, so 1 and 586 are divisors of 586)
586 / 2 = 293 (the remainder is 0, so 2 and 293 are divisors of 586)
586 / 3 = 195.33333333333 (the remainder is 1, so 3 is not a divisor of 586)
...
586 / 23 = 25.478260869565 (the remainder is 11, so 23 is not a divisor of 586)
586 / 24 = 24.416666666667 (the remainder is 10, so 24 is not a divisor of 586)