What are the divisors of 5708?

1, 2, 4, 1427, 2854, 5708

There is a total of 6 positive divisors.
The sum of these divisors is 9996.
The arithmetic mean is 1666.

4 even divisors

2, 4, 2854, 5708

2 odd divisors

1, 1427

How to compute the divisors of 5708?

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 5708 by each of the numbers from 1 to 5708 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)

5708 / 1 = 5708 (the remainder is 0, so 1 is a divisor of 5708)
5708 / 2 = 2854 (the remainder is 0, so 2 is a divisor of 5708)
5708 / 3 = 1902.6666666667 (the remainder is 2, so 3 is not a divisor of 5708)
...
5708 / 5707 = 1.0001752234098 (the remainder is 1, so 5707 is not a divisor of 5708)
5708 / 5708 = 1 (the remainder is 0, so 5708 is a divisor of 5708)

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 5708 (i.e. 75.551307070096). 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 $\frac{N}{d} = D$ )

5708 / 1 = 5708 (the remainder is 0, so 1 and 5708 are divisors of 5708)
5708 / 2 = 2854 (the remainder is 0, so 2 and 2854 are divisors of 5708)
5708 / 3 = 1902.6666666667 (the remainder is 2, so 3 is not a divisor of 5708)
...
5708 / 74 = 77.135135135135 (the remainder is 10, so 74 is not a divisor of 5708)
5708 / 75 = 76.106666666667 (the remainder is 8, so 75 is not a divisor of 5708)