What are the divisors of 5585?

1, 5, 1117, 5585

There is a total of 4 positive divisors.
The sum of these divisors is 6708.
The arithmetic mean is 1677.

4 odd divisors

1, 5, 1117, 5585

How to compute the divisors of 5585?

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 5585 by each of the numbers from 1 to 5585 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)

5585 / 1 = 5585 (the remainder is 0, so 1 is a divisor of 5585)
5585 / 2 = 2792.5 (the remainder is 1, so 2 is not a divisor of 5585)
5585 / 3 = 1861.6666666667 (the remainder is 2, so 3 is not a divisor of 5585)
...
5585 / 5584 = 1.0001790830946 (the remainder is 1, so 5584 is not a divisor of 5585)
5585 / 5585 = 1 (the remainder is 0, so 5585 is a divisor of 5585)

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 5585 (i.e. 74.732857566134). 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 $\frac{N}{d} = D$ )

5585 / 1 = 5585 (the remainder is 0, so 1 and 5585 are divisors of 5585)
5585 / 2 = 2792.5 (the remainder is 1, so 2 is not a divisor of 5585)
5585 / 3 = 1861.6666666667 (the remainder is 2, so 3 is not a divisor of 5585)
...
5585 / 73 = 76.506849315068 (the remainder is 37, so 73 is not a divisor of 5585)
5585 / 74 = 75.472972972973 (the remainder is 35, so 74 is not a divisor of 5585)