What are the divisors of 5524?

1, 2, 4, 1381, 2762, 5524

There is a total of 6 positive divisors.
The sum of these divisors is 9674.
The arithmetic mean is 1612.3333333333.

4 even divisors

2, 4, 2762, 5524

2 odd divisors

1, 1381

How to compute the divisors of 5524?

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 5524 by each of the numbers from 1 to 5524 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)

5524 / 1 = 5524 (the remainder is 0, so 1 is a divisor of 5524)
5524 / 2 = 2762 (the remainder is 0, so 2 is a divisor of 5524)
5524 / 3 = 1841.3333333333 (the remainder is 1, so 3 is not a divisor of 5524)
...
5524 / 5523 = 1.0001810610176 (the remainder is 1, so 5523 is not a divisor of 5524)
5524 / 5524 = 1 (the remainder is 0, so 5524 is a divisor of 5524)

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 5524 (i.e. 74.323616704248). 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 $\frac{N}{d} = D$ )

5524 / 1 = 5524 (the remainder is 0, so 1 and 5524 are divisors of 5524)
5524 / 2 = 2762 (the remainder is 0, so 2 and 2762 are divisors of 5524)
5524 / 3 = 1841.3333333333 (the remainder is 1, so 3 is not a divisor of 5524)
...
5524 / 73 = 75.671232876712 (the remainder is 49, so 73 is not a divisor of 5524)
5524 / 74 = 74.648648648649 (the remainder is 48, so 74 is not a divisor of 5524)