Question $1(60$ points$)$

This question requires you to write a MATLAB script that includes the following functions, and will perform

the steps listed below the functions. Do not use any built$-$in MATLAB functions for this task.

Functions:

$1.$ Write a function named Factors$($num$)$ that takes an integer and returns an array of all possible

factors of the num as well as the time $($in microseconds$)$ it took to compute it$.$ For example, if num is

$18,$ the function should return $1,2,3,6,9,$ and $18$ and computation time.

$2.$ Write a function named Factorial$($num$)$ that takes an integer as an argument and returns its

factorial as well as the time $($in microseconds$)$ it took to compute the factorial. For example, if num is

$5,$ the function should return $120(5!)$ and computation time.

$3.$ Write a function named PrimeNumbers$($num$)$ that takes an integer as an argument and returns an

array of all prime numbers less than or equal to num as well as the time $($in microseconds$)$ it took to

compute it$.$

Script: Your script should perform the following steps:

$1.$ After receiving input from the user, the program should check whether the input is between $500$ and

$1000.$ If the number passes this condition, the script should continue its other steps. If the condition is

not met, the script should output $$The input is not between $500$ and $1000$ and ask the user for input

again.

$2.$ In the next step, the program should check whether the input is indeed an integer and not a prime

number. If the input is not an integer, it should be rounded up to the next integer. If the input is a

prime number, add $1$ to make it non$-$prime.

$3.$ Call your Factors$($num$)$ function and print the array and computation time.

$4.$ Call your Factorial$($num$)$ function and print the result and computation time.

$5.$ Call your PrimeNumbers$($num$)$ function and print the result and computation time.

$6.$ plot all three times using a bar graph.