What are the divisors of 5707?

1, 13, 439, 5707

There is a total of 4 positive divisors.
The sum of these divisors is 6160.
The arithmetic mean is 1540.

4 odd divisors

1, 13, 439, 5707

How to compute the divisors of 5707?

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 5707 by each of the numbers from 1 to 5707 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)

5707 / 1 = 5707 (the remainder is 0, so 1 is a divisor of 5707)
5707 / 2 = 2853.5 (the remainder is 1, so 2 is not a divisor of 5707)
5707 / 3 = 1902.3333333333 (the remainder is 1, so 3 is not a divisor of 5707)
...
5707 / 5706 = 1.0001752541185 (the remainder is 1, so 5706 is not a divisor of 5707)
5707 / 5707 = 1 (the remainder is 0, so 5707 is a divisor of 5707)

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 5707 (i.e. 75.544688761024). 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 $\frac{N}{d} = D$ )

5707 / 1 = 5707 (the remainder is 0, so 1 and 5707 are divisors of 5707)
5707 / 2 = 2853.5 (the remainder is 1, so 2 is not a divisor of 5707)
5707 / 3 = 1902.3333333333 (the remainder is 1, so 3 is not a divisor of 5707)
...
5707 / 74 = 77.121621621622 (the remainder is 9, so 74 is not a divisor of 5707)
5707 / 75 = 76.093333333333 (the remainder is 7, so 75 is not a divisor of 5707)