What are the divisors of 5507?

1, 5507

There is a total of 2 positive divisors.
The sum of these divisors is 5508.
The arithmetic mean is 2754.

2 odd divisors

1, 5507

How to compute the divisors of 5507?

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 5507 by each of the numbers from 1 to 5507 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)

5507 / 1 = 5507 (the remainder is 0, so 1 is a divisor of 5507)
5507 / 2 = 2753.5 (the remainder is 1, so 2 is not a divisor of 5507)
5507 / 3 = 1835.6666666667 (the remainder is 2, so 3 is not a divisor of 5507)
...
5507 / 5506 = 1.0001816200509 (the remainder is 1, so 5506 is not a divisor of 5507)
5507 / 5507 = 1 (the remainder is 0, so 5507 is a divisor of 5507)

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 5507 (i.e. 74.209163854608). 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 $\frac{N}{d} = D$ )

5507 / 1 = 5507 (the remainder is 0, so 1 and 5507 are divisors of 5507)
5507 / 2 = 2753.5 (the remainder is 1, so 2 is not a divisor of 5507)
5507 / 3 = 1835.6666666667 (the remainder is 2, so 3 is not a divisor of 5507)
...
5507 / 73 = 75.438356164384 (the remainder is 32, so 73 is not a divisor of 5507)
5507 / 74 = 74.418918918919 (the remainder is 31, so 74 is not a divisor of 5507)