What are the divisors of 5526?

1, 2, 3, 6, 9, 18, 307, 614, 921, 1842, 2763, 5526

There is a total of 12 positive divisors.
The sum of these divisors is 12012.
The arithmetic mean is 1001.

6 even divisors

2, 6, 18, 614, 1842, 5526

6 odd divisors

1, 3, 9, 307, 921, 2763

How to compute the divisors of 5526?

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 5526 by each of the numbers from 1 to 5526 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)

5526 / 1 = 5526 (the remainder is 0, so 1 is a divisor of 5526)
5526 / 2 = 2763 (the remainder is 0, so 2 is a divisor of 5526)
5526 / 3 = 1842 (the remainder is 0, so 3 is a divisor of 5526)
...
5526 / 5525 = 1.0001809954751 (the remainder is 1, so 5525 is not a divisor of 5526)
5526 / 5526 = 1 (the remainder is 0, so 5526 is a divisor of 5526)

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 5526 (i.e. 74.337070160183). 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 $\frac{N}{d} = D$ )

5526 / 1 = 5526 (the remainder is 0, so 1 and 5526 are divisors of 5526)
5526 / 2 = 2763 (the remainder is 0, so 2 and 2763 are divisors of 5526)
5526 / 3 = 1842 (the remainder is 0, so 3 and 1842 are divisors of 5526)
...
5526 / 73 = 75.698630136986 (the remainder is 51, so 73 is not a divisor of 5526)
5526 / 74 = 74.675675675676 (the remainder is 50, so 74 is not a divisor of 5526)