What are the divisors of 5685?

1, 3, 5, 15, 379, 1137, 1895, 5685

There is a total of 8 positive divisors.
The sum of these divisors is 9120.
The arithmetic mean is 1140.

8 odd divisors

1, 3, 5, 15, 379, 1137, 1895, 5685

How to compute the divisors of 5685?

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 5685 by each of the numbers from 1 to 5685 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)

5685 / 1 = 5685 (the remainder is 0, so 1 is a divisor of 5685)
5685 / 2 = 2842.5 (the remainder is 1, so 2 is not a divisor of 5685)
5685 / 3 = 1895 (the remainder is 0, so 3 is a divisor of 5685)
...
5685 / 5684 = 1.0001759324419 (the remainder is 1, so 5684 is not a divisor of 5685)
5685 / 5685 = 1 (the remainder is 0, so 5685 is a divisor of 5685)

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 5685 (i.e. 75.398938984577). 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 $\frac{N}{d} = D$ )

5685 / 1 = 5685 (the remainder is 0, so 1 and 5685 are divisors of 5685)
5685 / 2 = 2842.5 (the remainder is 1, so 2 is not a divisor of 5685)
5685 / 3 = 1895 (the remainder is 0, so 3 and 1895 are divisors of 5685)
...
5685 / 74 = 76.824324324324 (the remainder is 61, so 74 is not a divisor of 5685)
5685 / 75 = 75.8 (the remainder is 60, so 75 is not a divisor of 5685)