What are the divisors of 5830?

1, 2, 5, 10, 11, 22, 53, 55, 106, 110, 265, 530, 583, 1166, 2915, 5830

There is a total of 16 positive divisors.
The sum of these divisors is 11664.
The arithmetic mean is 729.

8 even divisors

2, 10, 22, 106, 110, 530, 1166, 5830

8 odd divisors

1, 5, 11, 53, 55, 265, 583, 2915

How to compute the divisors of 5830?

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 5830 by each of the numbers from 1 to 5830 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)

5830 / 1 = 5830 (the remainder is 0, so 1 is a divisor of 5830)
5830 / 2 = 2915 (the remainder is 0, so 2 is a divisor of 5830)
5830 / 3 = 1943.3333333333 (the remainder is 1, so 3 is not a divisor of 5830)
...
5830 / 5829 = 1.000171556013 (the remainder is 1, so 5829 is not a divisor of 5830)
5830 / 5830 = 1 (the remainder is 0, so 5830 is a divisor of 5830)

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 5830 (i.e. 76.354436675284). 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 $\frac{N}{d} = D$ )

5830 / 1 = 5830 (the remainder is 0, so 1 and 5830 are divisors of 5830)
5830 / 2 = 2915 (the remainder is 0, so 2 and 2915 are divisors of 5830)
5830 / 3 = 1943.3333333333 (the remainder is 1, so 3 is not a divisor of 5830)
...
5830 / 75 = 77.733333333333 (the remainder is 55, so 75 is not a divisor of 5830)
5830 / 76 = 76.710526315789 (the remainder is 54, so 76 is not a divisor of 5830)