What are the divisors of 591?

1, 3, 197, 591

There is a total of 4 positive divisors.
The sum of these divisors is 792.
The arithmetic mean is 198.

4 odd divisors

1, 3, 197, 591

How to compute the divisors of 591?

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 591 by each of the numbers from 1 to 591 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)

591 / 1 = 591 (the remainder is 0, so 1 is a divisor of 591)
591 / 2 = 295.5 (the remainder is 1, so 2 is not a divisor of 591)
591 / 3 = 197 (the remainder is 0, so 3 is a divisor of 591)
...
591 / 590 = 1.0016949152542 (the remainder is 1, so 590 is not a divisor of 591)
591 / 591 = 1 (the remainder is 0, so 591 is a divisor of 591)

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 591 (i.e. 24.310491562286). 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 $\frac{N}{d} = D$ )

591 / 1 = 591 (the remainder is 0, so 1 and 591 are divisors of 591)
591 / 2 = 295.5 (the remainder is 1, so 2 is not a divisor of 591)
591 / 3 = 197 (the remainder is 0, so 3 and 197 are divisors of 591)
...
591 / 23 = 25.695652173913 (the remainder is 16, so 23 is not a divisor of 591)
591 / 24 = 24.625 (the remainder is 15, so 24 is not a divisor of 591)