What are the divisors of 5688?

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72, 79, 158, 237, 316, 474, 632, 711, 948, 1422, 1896, 2844, 5688

There is a total of 24 positive divisors.
The sum of these divisors is 15600.
The arithmetic mean is 650.

18 even divisors

2, 4, 6, 8, 12, 18, 24, 36, 72, 158, 316, 474, 632, 948, 1422, 1896, 2844, 5688

6 odd divisors

1, 3, 9, 79, 237, 711

How to compute the divisors of 5688?

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 5688 by each of the numbers from 1 to 5688 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)

5688 / 1 = 5688 (the remainder is 0, so 1 is a divisor of 5688)
5688 / 2 = 2844 (the remainder is 0, so 2 is a divisor of 5688)
5688 / 3 = 1896 (the remainder is 0, so 3 is a divisor of 5688)
...
5688 / 5687 = 1.0001758396343 (the remainder is 1, so 5687 is not a divisor of 5688)
5688 / 5688 = 1 (the remainder is 0, so 5688 is a divisor of 5688)

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 5688 (i.e. 75.418830539859). 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 $\frac{N}{d} = D$ )

5688 / 1 = 5688 (the remainder is 0, so 1 and 5688 are divisors of 5688)
5688 / 2 = 2844 (the remainder is 0, so 2 and 2844 are divisors of 5688)
5688 / 3 = 1896 (the remainder is 0, so 3 and 1896 are divisors of 5688)
...
5688 / 74 = 76.864864864865 (the remainder is 64, so 74 is not a divisor of 5688)
5688 / 75 = 75.84 (the remainder is 63, so 75 is not a divisor of 5688)