In this assignment, you are going to write a Haskell function named factors to find all proper factors of a

positive Integer.

Given a positive Integer value $n,$ a proper factor of $n$ is defined to be an Integer value i between $1$ to $n$

$($exclusively$)$ such that $n$ is divisible by $i$; that is$,$ the remainder of dividing $n$ by $i$ is zero $(0).$ Note that although

$n$ is divisible by both $1$ and $n,$ they are not proper factors of $n.$

The function factors has the following type signature:

factors :: Integer $[$Integer$]$

That is$,$ it takes an Integer as its only parameter and returns a list of Integers. The elements in the list are

all proper factors of the parameter, and they must be all unique and in ascending order.

Here are some examples:

factors $,$

$154,176,224,308,352,616,1232$

factors $,$

factors $9676[2,4,41,59,82,118,164,236,2419,4838]$

factors $1179[3,9,131,393]$

factors $4639[]$

Note that the output for the last example is an empty list since $4,639$ is a prime number and it has no proper

factor.

Download the three files $"$CSC$207$a$3.$hs$","$CSC$207$a$3$Tester.hs$",$ and $"$CSC$207$a$3$TestData.hs$"$ from

Canvas and save them in the same folder. The last two files are the tester program and the test data file,

respectively. Do not modify these two files. The first file is the file you will work on$.$ Note that you cannot

rename this file and you cannot change the name of the function $($otherwise the tester will not be able to pick

up your implementation$).$ However, you can change the names of the parameters if you like. Also note that

the first line is required for the tester to locate your code so do not modify it$.$

The file $"$CSC$207$a$3.$ hs$"$ contains a dummy implementation of the function that always returns a singleton list

with the input parameter as its only element $($since a value cannot be a proper factor of itself, it is always

incorrect$).$ The contents of the file $"$CSC$207$a$3.$hs$"$ is listed here for your reference: factors :: Integer $->[$Integer$]$

factors n $=[$n$]$