What are the divisors of 5696?

1, 2, 4, 8, 16, 32, 64, 89, 178, 356, 712, 1424, 2848, 5696

There is a total of 14 positive divisors.
The sum of these divisors is 11430.
The arithmetic mean is 816.42857142857.

12 even divisors

2, 4, 8, 16, 32, 64, 178, 356, 712, 1424, 2848, 5696

2 odd divisors

1, 89

How to compute the divisors of 5696?

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 5696 by each of the numbers from 1 to 5696 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)

5696 / 1 = 5696 (the remainder is 0, so 1 is a divisor of 5696)
5696 / 2 = 2848 (the remainder is 0, so 2 is a divisor of 5696)
5696 / 3 = 1898.6666666667 (the remainder is 2, so 3 is not a divisor of 5696)
...
5696 / 5695 = 1.0001755926251 (the remainder is 1, so 5695 is not a divisor of 5696)
5696 / 5696 = 1 (the remainder is 0, so 5696 is a divisor of 5696)

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 5696 (i.e. 75.471849056453). 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 $\frac{N}{d} = D$ )

5696 / 1 = 5696 (the remainder is 0, so 1 and 5696 are divisors of 5696)
5696 / 2 = 2848 (the remainder is 0, so 2 and 2848 are divisors of 5696)
5696 / 3 = 1898.6666666667 (the remainder is 2, so 3 is not a divisor of 5696)
...
5696 / 74 = 76.972972972973 (the remainder is 72, so 74 is not a divisor of 5696)
5696 / 75 = 75.946666666667 (the remainder is 71, so 75 is not a divisor of 5696)