What are the divisors of 5590?

1, 2, 5, 10, 13, 26, 43, 65, 86, 130, 215, 430, 559, 1118, 2795, 5590

There is a total of 16 positive divisors.
The sum of these divisors is 11088.
The arithmetic mean is 693.

8 even divisors

2, 10, 26, 86, 130, 430, 1118, 5590

8 odd divisors

1, 5, 13, 43, 65, 215, 559, 2795

How to compute the divisors of 5590?

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 5590 by each of the numbers from 1 to 5590 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)

5590 / 1 = 5590 (the remainder is 0, so 1 is a divisor of 5590)
5590 / 2 = 2795 (the remainder is 0, so 2 is a divisor of 5590)
5590 / 3 = 1863.3333333333 (the remainder is 1, so 3 is not a divisor of 5590)
...
5590 / 5589 = 1.0001789228842 (the remainder is 1, so 5589 is not a divisor of 5590)
5590 / 5590 = 1 (the remainder is 0, so 5590 is a divisor of 5590)

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 5590 (i.e. 74.766302570075). 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 $\frac{N}{d} = D$ )

5590 / 1 = 5590 (the remainder is 0, so 1 and 5590 are divisors of 5590)
5590 / 2 = 2795 (the remainder is 0, so 2 and 2795 are divisors of 5590)
5590 / 3 = 1863.3333333333 (the remainder is 1, so 3 is not a divisor of 5590)
...
5590 / 73 = 76.575342465753 (the remainder is 42, so 73 is not a divisor of 5590)
5590 / 74 = 75.540540540541 (the remainder is 40, so 74 is not a divisor of 5590)