What are the divisors of 5684?

1, 2, 4, 7, 14, 28, 29, 49, 58, 98, 116, 196, 203, 406, 812, 1421, 2842, 5684

There is a total of 18 positive divisors.
The sum of these divisors is 11970.
The arithmetic mean is 665.

12 even divisors

2, 4, 14, 28, 58, 98, 116, 196, 406, 812, 2842, 5684

6 odd divisors

1, 7, 29, 49, 203, 1421

How to compute the divisors of 5684?

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 5684 by each of the numbers from 1 to 5684 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)

5684 / 1 = 5684 (the remainder is 0, so 1 is a divisor of 5684)
5684 / 2 = 2842 (the remainder is 0, so 2 is a divisor of 5684)
5684 / 3 = 1894.6666666667 (the remainder is 2, so 3 is not a divisor of 5684)
...
5684 / 5683 = 1.0001759633996 (the remainder is 1, so 5683 is not a divisor of 5684)
5684 / 5684 = 1 (the remainder is 0, so 5684 is a divisor of 5684)

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 5684 (i.e. 75.392307299883). 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 $\frac{N}{d} = D$ )

5684 / 1 = 5684 (the remainder is 0, so 1 and 5684 are divisors of 5684)
5684 / 2 = 2842 (the remainder is 0, so 2 and 2842 are divisors of 5684)
5684 / 3 = 1894.6666666667 (the remainder is 2, so 3 is not a divisor of 5684)
...
5684 / 74 = 76.810810810811 (the remainder is 60, so 74 is not a divisor of 5684)
5684 / 75 = 75.786666666667 (the remainder is 59, so 75 is not a divisor of 5684)