What are the divisors of 589?

1, 19, 31, 589

There is a total of 4 positive divisors.
The sum of these divisors is 640.
The arithmetic mean is 160.

4 odd divisors

1, 19, 31, 589

How to compute the divisors of 589?

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 589 by each of the numbers from 1 to 589 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)

589 / 1 = 589 (the remainder is 0, so 1 is a divisor of 589)
589 / 2 = 294.5 (the remainder is 1, so 2 is not a divisor of 589)
589 / 3 = 196.33333333333 (the remainder is 1, so 3 is not a divisor of 589)
...
589 / 588 = 1.0017006802721 (the remainder is 1, so 588 is not a divisor of 589)
589 / 589 = 1 (the remainder is 0, so 589 is a divisor of 589)

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 589 (i.e. 24.269322199023). 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 $\frac{N}{d} = D$ )

589 / 1 = 589 (the remainder is 0, so 1 and 589 are divisors of 589)
589 / 2 = 294.5 (the remainder is 1, so 2 is not a divisor of 589)
589 / 3 = 196.33333333333 (the remainder is 1, so 3 is not a divisor of 589)
...
589 / 23 = 25.608695652174 (the remainder is 14, so 23 is not a divisor of 589)
589 / 24 = 24.541666666667 (the remainder is 13, so 24 is not a divisor of 589)