What are the divisors of 571?

1, 571

There is a total of 2 positive divisors.
The sum of these divisors is 572.
The arithmetic mean is 286.

2 odd divisors

1, 571

How to compute the divisors of 571?

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 571 by each of the numbers from 1 to 571 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)

571 / 1 = 571 (the remainder is 0, so 1 is a divisor of 571)
571 / 2 = 285.5 (the remainder is 1, so 2 is not a divisor of 571)
571 / 3 = 190.33333333333 (the remainder is 1, so 3 is not a divisor of 571)
...
571 / 570 = 1.0017543859649 (the remainder is 1, so 570 is not a divisor of 571)
571 / 571 = 1 (the remainder is 0, so 571 is a divisor of 571)

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 571 (i.e. 23.895606290697). 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 $\frac{N}{d} = D$ )

571 / 1 = 571 (the remainder is 0, so 1 and 571 are divisors of 571)
571 / 2 = 285.5 (the remainder is 1, so 2 is not a divisor of 571)
571 / 3 = 190.33333333333 (the remainder is 1, so 3 is not a divisor of 571)
...
571 / 22 = 25.954545454545 (the remainder is 21, so 22 is not a divisor of 571)
571 / 23 = 24.826086956522 (the remainder is 19, so 23 is not a divisor of 571)