What are the divisors of 5508?

1, 2, 3, 4, 6, 9, 12, 17, 18, 27, 34, 36, 51, 54, 68, 81, 102, 108, 153, 162, 204, 306, 324, 459, 612, 918, 1377, 1836, 2754, 5508

There is a total of 30 positive divisors.
The sum of these divisors is 15246.
The arithmetic mean is 508.2.

20 even divisors

2, 4, 6, 12, 18, 34, 36, 54, 68, 102, 108, 162, 204, 306, 324, 612, 918, 1836, 2754, 5508

10 odd divisors

1, 3, 9, 17, 27, 51, 81, 153, 459, 1377

How to compute the divisors of 5508?

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 5508 by each of the numbers from 1 to 5508 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)

5508 / 1 = 5508 (the remainder is 0, so 1 is a divisor of 5508)
5508 / 2 = 2754 (the remainder is 0, so 2 is a divisor of 5508)
5508 / 3 = 1836 (the remainder is 0, so 3 is a divisor of 5508)
...
5508 / 5507 = 1.000181587071 (the remainder is 1, so 5507 is not a divisor of 5508)
5508 / 5508 = 1 (the remainder is 0, so 5508 is a divisor of 5508)

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 5508 (i.e. 74.215901261118). 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 $\frac{N}{d} = D$ )

5508 / 1 = 5508 (the remainder is 0, so 1 and 5508 are divisors of 5508)
5508 / 2 = 2754 (the remainder is 0, so 2 and 2754 are divisors of 5508)
5508 / 3 = 1836 (the remainder is 0, so 3 and 1836 are divisors of 5508)
...
5508 / 73 = 75.452054794521 (the remainder is 33, so 73 is not a divisor of 5508)
5508 / 74 = 74.432432432432 (the remainder is 32, so 74 is not a divisor of 5508)