What are the divisors of 5528?

1, 2, 4, 8, 691, 1382, 2764, 5528

There is a total of 8 positive divisors.
The sum of these divisors is 10380.
The arithmetic mean is 1297.5.

6 even divisors

2, 4, 8, 1382, 2764, 5528

2 odd divisors

1, 691

How to compute the divisors of 5528?

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 5528 by each of the numbers from 1 to 5528 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)

5528 / 1 = 5528 (the remainder is 0, so 1 is a divisor of 5528)
5528 / 2 = 2764 (the remainder is 0, so 2 is a divisor of 5528)
5528 / 3 = 1842.6666666667 (the remainder is 2, so 3 is not a divisor of 5528)
...
5528 / 5527 = 1.0001809299801 (the remainder is 1, so 5527 is not a divisor of 5528)
5528 / 5528 = 1 (the remainder is 0, so 5528 is a divisor of 5528)

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 5528 (i.e. 74.350521181764). 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 $\frac{N}{d} = D$ )

5528 / 1 = 5528 (the remainder is 0, so 1 and 5528 are divisors of 5528)
5528 / 2 = 2764 (the remainder is 0, so 2 and 2764 are divisors of 5528)
5528 / 3 = 1842.6666666667 (the remainder is 2, so 3 is not a divisor of 5528)
...
5528 / 73 = 75.72602739726 (the remainder is 53, so 73 is not a divisor of 5528)
5528 / 74 = 74.702702702703 (the remainder is 52, so 74 is not a divisor of 5528)