What are the divisors of 5690?

1, 2, 5, 10, 569, 1138, 2845, 5690

There is a total of 8 positive divisors.
The sum of these divisors is 10260.
The arithmetic mean is 1282.5.

4 even divisors

2, 10, 1138, 5690

4 odd divisors

1, 5, 569, 2845

How to compute the divisors of 5690?

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 5690 by each of the numbers from 1 to 5690 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)

5690 / 1 = 5690 (the remainder is 0, so 1 is a divisor of 5690)
5690 / 2 = 2845 (the remainder is 0, so 2 is a divisor of 5690)
5690 / 3 = 1896.6666666667 (the remainder is 2, so 3 is not a divisor of 5690)
...
5690 / 5689 = 1.0001757778168 (the remainder is 1, so 5689 is not a divisor of 5690)
5690 / 5690 = 1 (the remainder is 0, so 5690 is a divisor of 5690)

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 5690 (i.e. 75.432088662584). 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 $\frac{N}{d} = D$ )

5690 / 1 = 5690 (the remainder is 0, so 1 and 5690 are divisors of 5690)
5690 / 2 = 2845 (the remainder is 0, so 2 and 2845 are divisors of 5690)
5690 / 3 = 1896.6666666667 (the remainder is 2, so 3 is not a divisor of 5690)
...
5690 / 74 = 76.891891891892 (the remainder is 66, so 74 is not a divisor of 5690)
5690 / 75 = 75.866666666667 (the remainder is 65, so 75 is not a divisor of 5690)