What are the divisors of 5566?

1, 2, 11, 22, 23, 46, 121, 242, 253, 506, 2783, 5566

There is a total of 12 positive divisors.
The sum of these divisors is 9576.
The arithmetic mean is 798.

6 even divisors

2, 22, 46, 242, 506, 5566

6 odd divisors

1, 11, 23, 121, 253, 2783

How to compute the divisors of 5566?

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 5566 by each of the numbers from 1 to 5566 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)

5566 / 1 = 5566 (the remainder is 0, so 1 is a divisor of 5566)
5566 / 2 = 2783 (the remainder is 0, so 2 is a divisor of 5566)
5566 / 3 = 1855.3333333333 (the remainder is 1, so 3 is not a divisor of 5566)
...
5566 / 5565 = 1.0001796945193 (the remainder is 1, so 5565 is not a divisor of 5566)
5566 / 5566 = 1 (the remainder is 0, so 5566 is a divisor of 5566)

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 5566 (i.e. 74.605629814378). 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 $\frac{N}{d} = D$ )

5566 / 1 = 5566 (the remainder is 0, so 1 and 5566 are divisors of 5566)
5566 / 2 = 2783 (the remainder is 0, so 2 and 2783 are divisors of 5566)
5566 / 3 = 1855.3333333333 (the remainder is 1, so 3 is not a divisor of 5566)
...
5566 / 73 = 76.246575342466 (the remainder is 18, so 73 is not a divisor of 5566)
5566 / 74 = 75.216216216216 (the remainder is 16, so 74 is not a divisor of 5566)