What are the divisors of 5666?

1, 2, 2833, 5666

There is a total of 4 positive divisors.
The sum of these divisors is 8502.
The arithmetic mean is 2125.5.

2 even divisors

2, 5666

2 odd divisors

1, 2833

How to compute the divisors of 5666?

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 5666 by each of the numbers from 1 to 5666 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)

5666 / 1 = 5666 (the remainder is 0, so 1 is a divisor of 5666)
5666 / 2 = 2833 (the remainder is 0, so 2 is a divisor of 5666)
5666 / 3 = 1888.6666666667 (the remainder is 2, so 3 is not a divisor of 5666)
...
5666 / 5665 = 1.0001765225066 (the remainder is 1, so 5665 is not a divisor of 5666)
5666 / 5666 = 1 (the remainder is 0, so 5666 is a divisor of 5666)

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 5666 (i.e. 75.272837066235). 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 $\frac{N}{d} = D$ )

5666 / 1 = 5666 (the remainder is 0, so 1 and 5666 are divisors of 5666)
5666 / 2 = 2833 (the remainder is 0, so 2 and 2833 are divisors of 5666)
5666 / 3 = 1888.6666666667 (the remainder is 2, so 3 is not a divisor of 5666)
...
5666 / 74 = 76.567567567568 (the remainder is 42, so 74 is not a divisor of 5666)
5666 / 75 = 75.546666666667 (the remainder is 41, so 75 is not a divisor of 5666)