What are the divisors of 5689?

1, 5689

There is a total of 2 positive divisors.
The sum of these divisors is 5690.
The arithmetic mean is 2845.

2 odd divisors

1, 5689

How to compute the divisors of 5689?

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 5689 by each of the numbers from 1 to 5689 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)

5689 / 1 = 5689 (the remainder is 0, so 1 is a divisor of 5689)
5689 / 2 = 2844.5 (the remainder is 1, so 2 is not a divisor of 5689)
5689 / 3 = 1896.3333333333 (the remainder is 1, so 3 is not a divisor of 5689)
...
5689 / 5688 = 1.0001758087201 (the remainder is 1, so 5688 is not a divisor of 5689)
5689 / 5689 = 1 (the remainder is 0, so 5689 is a divisor of 5689)

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 5689 (i.e. 75.425459892532). 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 $\frac{N}{d} = D$ )

5689 / 1 = 5689 (the remainder is 0, so 1 and 5689 are divisors of 5689)
5689 / 2 = 2844.5 (the remainder is 1, so 2 is not a divisor of 5689)
5689 / 3 = 1896.3333333333 (the remainder is 1, so 3 is not a divisor of 5689)
...
5689 / 74 = 76.878378378378 (the remainder is 65, so 74 is not a divisor of 5689)
5689 / 75 = 75.853333333333 (the remainder is 64, so 75 is not a divisor of 5689)