What are the divisors of 5798?

1, 2, 13, 26, 223, 446, 2899, 5798

There is a total of 8 positive divisors.
The sum of these divisors is 9408.
The arithmetic mean is 1176.

4 even divisors

2, 26, 446, 5798

4 odd divisors

1, 13, 223, 2899

How to compute the divisors of 5798?

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 5798 by each of the numbers from 1 to 5798 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)

5798 / 1 = 5798 (the remainder is 0, so 1 is a divisor of 5798)
5798 / 2 = 2899 (the remainder is 0, so 2 is a divisor of 5798)
5798 / 3 = 1932.6666666667 (the remainder is 2, so 3 is not a divisor of 5798)
...
5798 / 5797 = 1.0001725030188 (the remainder is 1, so 5797 is not a divisor of 5798)
5798 / 5798 = 1 (the remainder is 0, so 5798 is a divisor of 5798)

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 5798 (i.e. 76.144599283206). 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 $\frac{N}{d} = D$ )

5798 / 1 = 5798 (the remainder is 0, so 1 and 5798 are divisors of 5798)
5798 / 2 = 2899 (the remainder is 0, so 2 and 2899 are divisors of 5798)
5798 / 3 = 1932.6666666667 (the remainder is 2, so 3 is not a divisor of 5798)
...
5798 / 75 = 77.306666666667 (the remainder is 23, so 75 is not a divisor of 5798)
5798 / 76 = 76.289473684211 (the remainder is 22, so 76 is not a divisor of 5798)