What are the divisors of 579?

1, 3, 193, 579

There is a total of 4 positive divisors.
The sum of these divisors is 776.
The arithmetic mean is 194.

4 odd divisors

1, 3, 193, 579

How to compute the divisors of 579?

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 579 by each of the numbers from 1 to 579 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)

579 / 1 = 579 (the remainder is 0, so 1 is a divisor of 579)
579 / 2 = 289.5 (the remainder is 1, so 2 is not a divisor of 579)
579 / 3 = 193 (the remainder is 0, so 3 is a divisor of 579)
...
579 / 578 = 1.0017301038062 (the remainder is 1, so 578 is not a divisor of 579)
579 / 579 = 1 (the remainder is 0, so 579 is a divisor of 579)

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 579 (i.e. 24.062418831032). 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 $\frac{N}{d} = D$ )

579 / 1 = 579 (the remainder is 0, so 1 and 579 are divisors of 579)
579 / 2 = 289.5 (the remainder is 1, so 2 is not a divisor of 579)
579 / 3 = 193 (the remainder is 0, so 3 and 193 are divisors of 579)
...
579 / 23 = 25.173913043478 (the remainder is 4, so 23 is not a divisor of 579)
579 / 24 = 24.125 (the remainder is 3, so 24 is not a divisor of 579)