What are the divisors of 5518?

1, 2, 31, 62, 89, 178, 2759, 5518

There is a total of 8 positive divisors.
The sum of these divisors is 8640.
The arithmetic mean is 1080.

4 even divisors

2, 62, 178, 5518

4 odd divisors

1, 31, 89, 2759

How to compute the divisors of 5518?

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 5518 by each of the numbers from 1 to 5518 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)

5518 / 1 = 5518 (the remainder is 0, so 1 is a divisor of 5518)
5518 / 2 = 2759 (the remainder is 0, so 2 is a divisor of 5518)
5518 / 3 = 1839.3333333333 (the remainder is 1, so 3 is not a divisor of 5518)
...
5518 / 5517 = 1.00018125793 (the remainder is 1, so 5517 is not a divisor of 5518)
5518 / 5518 = 1 (the remainder is 0, so 5518 is a divisor of 5518)

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 5518 (i.e. 74.283241717093). 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 $\frac{N}{d} = D$ )

5518 / 1 = 5518 (the remainder is 0, so 1 and 5518 are divisors of 5518)
5518 / 2 = 2759 (the remainder is 0, so 2 and 2759 are divisors of 5518)
5518 / 3 = 1839.3333333333 (the remainder is 1, so 3 is not a divisor of 5518)
...
5518 / 73 = 75.58904109589 (the remainder is 43, so 73 is not a divisor of 5518)
5518 / 74 = 74.567567567568 (the remainder is 42, so 74 is not a divisor of 5518)