What are the divisors of 5512?

1, 2, 4, 8, 13, 26, 52, 53, 104, 106, 212, 424, 689, 1378, 2756, 5512

There is a total of 16 positive divisors.
The sum of these divisors is 11340.
The arithmetic mean is 708.75.

12 even divisors

2, 4, 8, 26, 52, 104, 106, 212, 424, 1378, 2756, 5512

4 odd divisors

1, 13, 53, 689

How to compute the divisors of 5512?

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 5512 by each of the numbers from 1 to 5512 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)

5512 / 1 = 5512 (the remainder is 0, so 1 is a divisor of 5512)
5512 / 2 = 2756 (the remainder is 0, so 2 is a divisor of 5512)
5512 / 3 = 1837.3333333333 (the remainder is 1, so 3 is not a divisor of 5512)
...
5512 / 5511 = 1.0001814552713 (the remainder is 1, so 5511 is not a divisor of 5512)
5512 / 5512 = 1 (the remainder is 0, so 5512 is a divisor of 5512)

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 5512 (i.e. 74.242844773082). 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 $\frac{N}{d} = D$ )

5512 / 1 = 5512 (the remainder is 0, so 1 and 5512 are divisors of 5512)
5512 / 2 = 2756 (the remainder is 0, so 2 and 2756 are divisors of 5512)
5512 / 3 = 1837.3333333333 (the remainder is 1, so 3 is not a divisor of 5512)
...
5512 / 73 = 75.506849315068 (the remainder is 37, so 73 is not a divisor of 5512)
5512 / 74 = 74.486486486486 (the remainder is 36, so 74 is not a divisor of 5512)