What are the divisors of 5848?

1, 2, 4, 8, 17, 34, 43, 68, 86, 136, 172, 344, 731, 1462, 2924, 5848

There is a total of 16 positive divisors.
The sum of these divisors is 11880.
The arithmetic mean is 742.5.

12 even divisors

2, 4, 8, 34, 68, 86, 136, 172, 344, 1462, 2924, 5848

4 odd divisors

1, 17, 43, 731

How to compute the divisors of 5848?

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 5848 by each of the numbers from 1 to 5848 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)

5848 / 1 = 5848 (the remainder is 0, so 1 is a divisor of 5848)
5848 / 2 = 2924 (the remainder is 0, so 2 is a divisor of 5848)
5848 / 3 = 1949.3333333333 (the remainder is 1, so 3 is not a divisor of 5848)
...
5848 / 5847 = 1.0001710278775 (the remainder is 1, so 5847 is not a divisor of 5848)
5848 / 5848 = 1 (the remainder is 0, so 5848 is a divisor of 5848)

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 5848 (i.e. 76.472217177221). 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 $\frac{N}{d} = D$ )

5848 / 1 = 5848 (the remainder is 0, so 1 and 5848 are divisors of 5848)
5848 / 2 = 2924 (the remainder is 0, so 2 and 2924 are divisors of 5848)
5848 / 3 = 1949.3333333333 (the remainder is 1, so 3 is not a divisor of 5848)
...
5848 / 75 = 77.973333333333 (the remainder is 73, so 75 is not a divisor of 5848)
5848 / 76 = 76.947368421053 (the remainder is 72, so 76 is not a divisor of 5848)