What are the divisors of 593?

1, 593

There is a total of 2 positive divisors.
The sum of these divisors is 594.
The arithmetic mean is 297.

2 odd divisors

1, 593

How to compute the divisors of 593?

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 593 by each of the numbers from 1 to 593 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)

593 / 1 = 593 (the remainder is 0, so 1 is a divisor of 593)
593 / 2 = 296.5 (the remainder is 1, so 2 is not a divisor of 593)
593 / 3 = 197.66666666667 (the remainder is 2, so 3 is not a divisor of 593)
...
593 / 592 = 1.0016891891892 (the remainder is 1, so 592 is not a divisor of 593)
593 / 593 = 1 (the remainder is 0, so 593 is a divisor of 593)

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 593 (i.e. 24.351591323772). 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 $\frac{N}{d} = D$ )

593 / 1 = 593 (the remainder is 0, so 1 and 593 are divisors of 593)
593 / 2 = 296.5 (the remainder is 1, so 2 is not a divisor of 593)
593 / 3 = 197.66666666667 (the remainder is 2, so 3 is not a divisor of 593)
...
593 / 23 = 25.782608695652 (the remainder is 18, so 23 is not a divisor of 593)
593 / 24 = 24.708333333333 (the remainder is 17, so 24 is not a divisor of 593)