What are the divisors of 566?

1, 2, 283, 566

There is a total of 4 positive divisors.
The sum of these divisors is 852.
The arithmetic mean is 213.

2 even divisors

2, 566

2 odd divisors

1, 283

How to compute the divisors of 566?

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 566 by each of the numbers from 1 to 566 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)

566 / 1 = 566 (the remainder is 0, so 1 is a divisor of 566)
566 / 2 = 283 (the remainder is 0, so 2 is a divisor of 566)
566 / 3 = 188.66666666667 (the remainder is 2, so 3 is not a divisor of 566)
...
566 / 565 = 1.0017699115044 (the remainder is 1, so 565 is not a divisor of 566)
566 / 566 = 1 (the remainder is 0, so 566 is a divisor of 566)

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 566 (i.e. 23.790754506741). 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 $\frac{N}{d} = D$ )

566 / 1 = 566 (the remainder is 0, so 1 and 566 are divisors of 566)
566 / 2 = 283 (the remainder is 0, so 2 and 283 are divisors of 566)
566 / 3 = 188.66666666667 (the remainder is 2, so 3 is not a divisor of 566)
...
566 / 22 = 25.727272727273 (the remainder is 16, so 22 is not a divisor of 566)
566 / 23 = 24.608695652174 (the remainder is 14, so 23 is not a divisor of 566)