What are the divisors of 572?

1, 2, 4, 11, 13, 22, 26, 44, 52, 143, 286, 572

There is a total of 12 positive divisors.
The sum of these divisors is 1176.
The arithmetic mean is 98.

8 even divisors

2, 4, 22, 26, 44, 52, 286, 572

4 odd divisors

1, 11, 13, 143

How to compute the divisors of 572?

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 572 by each of the numbers from 1 to 572 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)

572 / 1 = 572 (the remainder is 0, so 1 is a divisor of 572)
572 / 2 = 286 (the remainder is 0, so 2 is a divisor of 572)
572 / 3 = 190.66666666667 (the remainder is 2, so 3 is not a divisor of 572)
...
572 / 571 = 1.0017513134851 (the remainder is 1, so 571 is not a divisor of 572)
572 / 572 = 1 (the remainder is 0, so 572 is a divisor of 572)

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 572 (i.e. 23.916521486203). 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 $\frac{N}{d} = D$ )

572 / 1 = 572 (the remainder is 0, so 1 and 572 are divisors of 572)
572 / 2 = 286 (the remainder is 0, so 2 and 286 are divisors of 572)
572 / 3 = 190.66666666667 (the remainder is 2, so 3 is not a divisor of 572)
...
572 / 22 = 26 (the remainder is 0, so 22 and 26 are divisors of 572)
572 / 23 = 24.869565217391 (the remainder is 20, so 23 is not a divisor of 572)