What are the divisors of 5828?

1, 2, 4, 31, 47, 62, 94, 124, 188, 1457, 2914, 5828

There is a total of 12 positive divisors.
The sum of these divisors is 10752.
The arithmetic mean is 896.

8 even divisors

2, 4, 62, 94, 124, 188, 2914, 5828

4 odd divisors

1, 31, 47, 1457

How to compute the divisors of 5828?

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 5828 by each of the numbers from 1 to 5828 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)

5828 / 1 = 5828 (the remainder is 0, so 1 is a divisor of 5828)
5828 / 2 = 2914 (the remainder is 0, so 2 is a divisor of 5828)
5828 / 3 = 1942.6666666667 (the remainder is 2, so 3 is not a divisor of 5828)
...
5828 / 5827 = 1.0001716148962 (the remainder is 1, so 5827 is not a divisor of 5828)
5828 / 5828 = 1 (the remainder is 0, so 5828 is a divisor of 5828)

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 5828 (i.e. 76.341338735969). 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 $\frac{N}{d} = D$ )

5828 / 1 = 5828 (the remainder is 0, so 1 and 5828 are divisors of 5828)
5828 / 2 = 2914 (the remainder is 0, so 2 and 2914 are divisors of 5828)
5828 / 3 = 1942.6666666667 (the remainder is 2, so 3 is not a divisor of 5828)
...
5828 / 75 = 77.706666666667 (the remainder is 53, so 75 is not a divisor of 5828)
5828 / 76 = 76.684210526316 (the remainder is 52, so 76 is not a divisor of 5828)