What are the divisors of 5809?

1, 37, 157, 5809

There is a total of 4 positive divisors.
The sum of these divisors is 6004.
The arithmetic mean is 1501.

4 odd divisors

1, 37, 157, 5809

How to compute the divisors of 5809?

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 5809 by each of the numbers from 1 to 5809 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)

5809 / 1 = 5809 (the remainder is 0, so 1 is a divisor of 5809)
5809 / 2 = 2904.5 (the remainder is 1, so 2 is not a divisor of 5809)
5809 / 3 = 1936.3333333333 (the remainder is 1, so 3 is not a divisor of 5809)
...
5809 / 5808 = 1.0001721763085 (the remainder is 1, so 5808 is not a divisor of 5809)
5809 / 5809 = 1 (the remainder is 0, so 5809 is a divisor of 5809)

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 5809 (i.e. 76.216796049165). 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 $\frac{N}{d} = D$ )

5809 / 1 = 5809 (the remainder is 0, so 1 and 5809 are divisors of 5809)
5809 / 2 = 2904.5 (the remainder is 1, so 2 is not a divisor of 5809)
5809 / 3 = 1936.3333333333 (the remainder is 1, so 3 is not a divisor of 5809)
...
5809 / 75 = 77.453333333333 (the remainder is 34, so 75 is not a divisor of 5809)
5809 / 76 = 76.434210526316 (the remainder is 33, so 76 is not a divisor of 5809)