What are the divisors of 5506?

1, 2, 2753, 5506

There is a total of 4 positive divisors.
The sum of these divisors is 8262.
The arithmetic mean is 2065.5.

2 even divisors

2, 5506

2 odd divisors

1, 2753

How to compute the divisors of 5506?

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 5506 by each of the numbers from 1 to 5506 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)

5506 / 1 = 5506 (the remainder is 0, so 1 is a divisor of 5506)
5506 / 2 = 2753 (the remainder is 0, so 2 is a divisor of 5506)
5506 / 3 = 1835.3333333333 (the remainder is 1, so 3 is not a divisor of 5506)
...
5506 / 5505 = 1.0001816530427 (the remainder is 1, so 5505 is not a divisor of 5506)
5506 / 5506 = 1 (the remainder is 0, so 5506 is a divisor of 5506)

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 5506 (i.e. 74.202425836357). 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 $\frac{N}{d} = D$ )

5506 / 1 = 5506 (the remainder is 0, so 1 and 5506 are divisors of 5506)
5506 / 2 = 2753 (the remainder is 0, so 2 and 2753 are divisors of 5506)
5506 / 3 = 1835.3333333333 (the remainder is 1, so 3 is not a divisor of 5506)
...
5506 / 73 = 75.424657534247 (the remainder is 31, so 73 is not a divisor of 5506)
5506 / 74 = 74.405405405405 (the remainder is 30, so 74 is not a divisor of 5506)