What are the divisors of 5839?

1, 5839

There is a total of 2 positive divisors.
The sum of these divisors is 5840.
The arithmetic mean is 2920.

2 odd divisors

1, 5839

How to compute the divisors of 5839?

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 5839 by each of the numbers from 1 to 5839 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)

5839 / 1 = 5839 (the remainder is 0, so 1 is a divisor of 5839)
5839 / 2 = 2919.5 (the remainder is 1, so 2 is not a divisor of 5839)
5839 / 3 = 1946.3333333333 (the remainder is 1, so 3 is not a divisor of 5839)
...
5839 / 5838 = 1.0001712915382 (the remainder is 1, so 5838 is not a divisor of 5839)
5839 / 5839 = 1 (the remainder is 0, so 5839 is a divisor of 5839)

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 5839 (i.e. 76.413349619029). 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 $\frac{N}{d} = D$ )

5839 / 1 = 5839 (the remainder is 0, so 1 and 5839 are divisors of 5839)
5839 / 2 = 2919.5 (the remainder is 1, so 2 is not a divisor of 5839)
5839 / 3 = 1946.3333333333 (the remainder is 1, so 3 is not a divisor of 5839)
...
5839 / 75 = 77.853333333333 (the remainder is 64, so 75 is not a divisor of 5839)
5839 / 76 = 76.828947368421 (the remainder is 63, so 76 is not a divisor of 5839)