What are the divisors of 590?

1, 2, 5, 10, 59, 118, 295, 590

There is a total of 8 positive divisors.
The sum of these divisors is 1080.
The arithmetic mean is 135.

4 even divisors

2, 10, 118, 590

4 odd divisors

1, 5, 59, 295

How to compute the divisors of 590?

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 590 by each of the numbers from 1 to 590 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)

590 / 1 = 590 (the remainder is 0, so 1 is a divisor of 590)
590 / 2 = 295 (the remainder is 0, so 2 is a divisor of 590)
590 / 3 = 196.66666666667 (the remainder is 2, so 3 is not a divisor of 590)
...
590 / 589 = 1.0016977928693 (the remainder is 1, so 589 is not a divisor of 590)
590 / 590 = 1 (the remainder is 0, so 590 is a divisor of 590)

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 590 (i.e. 24.289915602982). 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 $\frac{N}{d} = D$ )

590 / 1 = 590 (the remainder is 0, so 1 and 590 are divisors of 590)
590 / 2 = 295 (the remainder is 0, so 2 and 295 are divisors of 590)
590 / 3 = 196.66666666667 (the remainder is 2, so 3 is not a divisor of 590)
...
590 / 23 = 25.652173913043 (the remainder is 15, so 23 is not a divisor of 590)
590 / 24 = 24.583333333333 (the remainder is 14, so 24 is not a divisor of 590)