What are the divisors of 5589?

1, 3, 9, 23, 27, 69, 81, 207, 243, 621, 1863, 5589

There is a total of 12 positive divisors.
The sum of these divisors is 8736.
The arithmetic mean is 728.

12 odd divisors

1, 3, 9, 23, 27, 69, 81, 207, 243, 621, 1863, 5589

How to compute the divisors of 5589?

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 5589 by each of the numbers from 1 to 5589 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)

5589 / 1 = 5589 (the remainder is 0, so 1 is a divisor of 5589)
5589 / 2 = 2794.5 (the remainder is 1, so 2 is not a divisor of 5589)
5589 / 3 = 1863 (the remainder is 0, so 3 is a divisor of 5589)
...
5589 / 5588 = 1.0001789549034 (the remainder is 1, so 5588 is not a divisor of 5589)
5589 / 5589 = 1 (the remainder is 0, so 5589 is a divisor of 5589)

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 5589 (i.e. 74.759614766263). 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 $\frac{N}{d} = D$ )

5589 / 1 = 5589 (the remainder is 0, so 1 and 5589 are divisors of 5589)
5589 / 2 = 2794.5 (the remainder is 1, so 2 is not a divisor of 5589)
5589 / 3 = 1863 (the remainder is 0, so 3 and 1863 are divisors of 5589)
...
5589 / 73 = 76.561643835616 (the remainder is 41, so 73 is not a divisor of 5589)
5589 / 74 = 75.527027027027 (the remainder is 39, so 74 is not a divisor of 5589)