What are the divisors of 5728?

1, 2, 4, 8, 16, 32, 179, 358, 716, 1432, 2864, 5728

There is a total of 12 positive divisors.
The sum of these divisors is 11340.
The arithmetic mean is 945.

10 even divisors

2, 4, 8, 16, 32, 358, 716, 1432, 2864, 5728

2 odd divisors

1, 179

How to compute the divisors of 5728?

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 5728 by each of the numbers from 1 to 5728 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)

5728 / 1 = 5728 (the remainder is 0, so 1 is a divisor of 5728)
5728 / 2 = 2864 (the remainder is 0, so 2 is a divisor of 5728)
5728 / 3 = 1909.3333333333 (the remainder is 1, so 3 is not a divisor of 5728)
...
5728 / 5727 = 1.0001746114894 (the remainder is 1, so 5727 is not a divisor of 5728)
5728 / 5728 = 1 (the remainder is 0, so 5728 is a divisor of 5728)

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 5728 (i.e. 75.683551713698). 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 $\frac{N}{d} = D$ )

5728 / 1 = 5728 (the remainder is 0, so 1 and 5728 are divisors of 5728)
5728 / 2 = 2864 (the remainder is 0, so 2 and 2864 are divisors of 5728)
5728 / 3 = 1909.3333333333 (the remainder is 1, so 3 is not a divisor of 5728)
...
5728 / 74 = 77.405405405405 (the remainder is 30, so 74 is not a divisor of 5728)
5728 / 75 = 76.373333333333 (the remainder is 28, so 75 is not a divisor of 5728)