What are the divisors of 5509?

1, 7, 787, 5509

There is a total of 4 positive divisors.
The sum of these divisors is 6304.
The arithmetic mean is 1576.

4 odd divisors

1, 7, 787, 5509

How to compute the divisors of 5509?

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 5509 by each of the numbers from 1 to 5509 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)

5509 / 1 = 5509 (the remainder is 0, so 1 is a divisor of 5509)
5509 / 2 = 2754.5 (the remainder is 1, so 2 is not a divisor of 5509)
5509 / 3 = 1836.3333333333 (the remainder is 1, so 3 is not a divisor of 5509)
...
5509 / 5508 = 1.0001815541031 (the remainder is 1, so 5508 is not a divisor of 5509)
5509 / 5509 = 1 (the remainder is 0, so 5509 is a divisor of 5509)

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 5509 (i.e. 74.222638056054). 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 $\frac{N}{d} = D$ )

5509 / 1 = 5509 (the remainder is 0, so 1 and 5509 are divisors of 5509)
5509 / 2 = 2754.5 (the remainder is 1, so 2 is not a divisor of 5509)
5509 / 3 = 1836.3333333333 (the remainder is 1, so 3 is not a divisor of 5509)
...
5509 / 73 = 75.465753424658 (the remainder is 34, so 73 is not a divisor of 5509)
5509 / 74 = 74.445945945946 (the remainder is 33, so 74 is not a divisor of 5509)