What are the divisors of 5489?

1, 11, 499, 5489

There is a total of 4 positive divisors.
The sum of these divisors is 6000.
The arithmetic mean is 1500.

4 odd divisors

1, 11, 499, 5489

How to compute the divisors of 5489?

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 5489 by each of the numbers from 1 to 5489 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)

5489 / 1 = 5489 (the remainder is 0, so 1 is a divisor of 5489)
5489 / 2 = 2744.5 (the remainder is 1, so 2 is not a divisor of 5489)
5489 / 3 = 1829.6666666667 (the remainder is 2, so 3 is not a divisor of 5489)
...
5489 / 5488 = 1.0001822157434 (the remainder is 1, so 5488 is not a divisor of 5489)
5489 / 5489 = 1 (the remainder is 0, so 5489 is a divisor of 5489)

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 5489 (i.e. 74.087785767966). 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 $\frac{N}{d} = D$ )

5489 / 1 = 5489 (the remainder is 0, so 1 and 5489 are divisors of 5489)
5489 / 2 = 2744.5 (the remainder is 1, so 2 is not a divisor of 5489)
5489 / 3 = 1829.6666666667 (the remainder is 2, so 3 is not a divisor of 5489)
...
5489 / 73 = 75.191780821918 (the remainder is 14, so 73 is not a divisor of 5489)
5489 / 74 = 74.175675675676 (the remainder is 13, so 74 is not a divisor of 5489)