What are the divisors of 5648?

1, 2, 4, 8, 16, 353, 706, 1412, 2824, 5648

There is a total of 10 positive divisors.
The sum of these divisors is 10974.
The arithmetic mean is 1097.4.

8 even divisors

2, 4, 8, 16, 706, 1412, 2824, 5648

2 odd divisors

1, 353

How to compute the divisors of 5648?

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 5648 by each of the numbers from 1 to 5648 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)

5648 / 1 = 5648 (the remainder is 0, so 1 is a divisor of 5648)
5648 / 2 = 2824 (the remainder is 0, so 2 is a divisor of 5648)
5648 / 3 = 1882.6666666667 (the remainder is 2, so 3 is not a divisor of 5648)
...
5648 / 5647 = 1.000177085178 (the remainder is 1, so 5647 is not a divisor of 5648)
5648 / 5648 = 1 (the remainder is 0, so 5648 is a divisor of 5648)

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 5648 (i.e. 75.153176912224). 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 $\frac{N}{d} = D$ )

5648 / 1 = 5648 (the remainder is 0, so 1 and 5648 are divisors of 5648)
5648 / 2 = 2824 (the remainder is 0, so 2 and 2824 are divisors of 5648)
5648 / 3 = 1882.6666666667 (the remainder is 2, so 3 is not a divisor of 5648)
...
5648 / 74 = 76.324324324324 (the remainder is 24, so 74 is not a divisor of 5648)
5648 / 75 = 75.306666666667 (the remainder is 23, so 75 is not a divisor of 5648)