What are the divisors of 5826?

1, 2, 3, 6, 971, 1942, 2913, 5826

There is a total of 8 positive divisors.
The sum of these divisors is 11664.
The arithmetic mean is 1458.

4 even divisors

2, 6, 1942, 5826

4 odd divisors

1, 3, 971, 2913

How to compute the divisors of 5826?

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 5826 by each of the numbers from 1 to 5826 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)

5826 / 1 = 5826 (the remainder is 0, so 1 is a divisor of 5826)
5826 / 2 = 2913 (the remainder is 0, so 2 is a divisor of 5826)
5826 / 3 = 1942 (the remainder is 0, so 3 is a divisor of 5826)
...
5826 / 5825 = 1.0001716738197 (the remainder is 1, so 5825 is not a divisor of 5826)
5826 / 5826 = 1 (the remainder is 0, so 5826 is a divisor of 5826)

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 5826 (i.e. 76.328238549046). 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 $\frac{N}{d} = D$ )

5826 / 1 = 5826 (the remainder is 0, so 1 and 5826 are divisors of 5826)
5826 / 2 = 2913 (the remainder is 0, so 2 and 2913 are divisors of 5826)
5826 / 3 = 1942 (the remainder is 0, so 3 and 1942 are divisors of 5826)
...
5826 / 75 = 77.68 (the remainder is 51, so 75 is not a divisor of 5826)
5826 / 76 = 76.657894736842 (the remainder is 50, so 76 is not a divisor of 5826)