What are the divisors of 5836?

1, 2, 4, 1459, 2918, 5836

There is a total of 6 positive divisors.
The sum of these divisors is 10220.
The arithmetic mean is 1703.3333333333.

4 even divisors

2, 4, 2918, 5836

2 odd divisors

1, 1459

How to compute the divisors of 5836?

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 5836 by each of the numbers from 1 to 5836 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)

5836 / 1 = 5836 (the remainder is 0, so 1 is a divisor of 5836)
5836 / 2 = 2918 (the remainder is 0, so 2 is a divisor of 5836)
5836 / 3 = 1945.3333333333 (the remainder is 1, so 3 is not a divisor of 5836)
...
5836 / 5835 = 1.0001713796058 (the remainder is 1, so 5835 is not a divisor of 5836)
5836 / 5836 = 1 (the remainder is 0, so 5836 is a divisor of 5836)

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 5836 (i.e. 76.393717019137). 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 $\frac{N}{d} = D$ )

5836 / 1 = 5836 (the remainder is 0, so 1 and 5836 are divisors of 5836)
5836 / 2 = 2918 (the remainder is 0, so 2 and 2918 are divisors of 5836)
5836 / 3 = 1945.3333333333 (the remainder is 1, so 3 is not a divisor of 5836)
...
5836 / 75 = 77.813333333333 (the remainder is 61, so 75 is not a divisor of 5836)
5836 / 76 = 76.789473684211 (the remainder is 60, so 76 is not a divisor of 5836)