What are the divisors of 5586?

1, 2, 3, 6, 7, 14, 19, 21, 38, 42, 49, 57, 98, 114, 133, 147, 266, 294, 399, 798, 931, 1862, 2793, 5586

There is a total of 24 positive divisors.
The sum of these divisors is 13680.
The arithmetic mean is 570.

12 even divisors

2, 6, 14, 38, 42, 98, 114, 266, 294, 798, 1862, 5586

12 odd divisors

1, 3, 7, 19, 21, 49, 57, 133, 147, 399, 931, 2793

How to compute the divisors of 5586?

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 5586 by each of the numbers from 1 to 5586 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)

5586 / 1 = 5586 (the remainder is 0, so 1 is a divisor of 5586)
5586 / 2 = 2793 (the remainder is 0, so 2 is a divisor of 5586)
5586 / 3 = 1862 (the remainder is 0, so 3 is a divisor of 5586)
...
5586 / 5585 = 1.0001790510295 (the remainder is 1, so 5585 is not a divisor of 5586)
5586 / 5586 = 1 (the remainder is 0, so 5586 is a divisor of 5586)

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 5586 (i.e. 74.739547764219). 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 $\frac{N}{d} = D$ )

5586 / 1 = 5586 (the remainder is 0, so 1 and 5586 are divisors of 5586)
5586 / 2 = 2793 (the remainder is 0, so 2 and 2793 are divisors of 5586)
5586 / 3 = 1862 (the remainder is 0, so 3 and 1862 are divisors of 5586)
...
5586 / 73 = 76.520547945205 (the remainder is 38, so 73 is not a divisor of 5586)
5586 / 74 = 75.486486486486 (the remainder is 36, so 74 is not a divisor of 5586)