Question $3$: Create a program that checks whether a number $($between $1$ and $5000,$ exclusive$)$ is a prime number and displays the total number of factors if it is not a prime number. Use the screenshot as a reference. $(30$ pts $.)$

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Prime Number Checker

Please enter an integer between $1$ and $5000$: $1$

Invalid integer. Please try again.

Please enter an integer between $1$ and $5000$: $2$

$2\}\backslash$mathrm$\{$ is a prime number.

Try again? $($y$/$n$)$: y

Please enter an integer between $1$ and $5000$: $3$

$3$ is a prime number.

Try again? $($y$/$n$)$: y

Please enter an integer between $1$ and $5000$: $4$

$4$ is NOT a prime number.

It has $3$ factors.

Try again? $($y$/$n$)$: y

Please enter an integer between $1$ and $5000$: $6$

$6$ is NOT a prime number.

It has $4$ factors.

Try again? $($y$/$n$)$: n

Bye!

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$(3$a$)$ A prime number is only divisible by two factors $(1$ and itself$).$ For example, $7$ is a prime number because it is only divisible by $1$ and $7.$ If the number is not a prime number, the program should display its number of factors. For example, $6$ has four factors $(1,2,3,$ and $6).(4$ pts$.)$

$(3$b$)$ Store the code that gets a valid integer for this program in its own function. $(8$ pts$.)$

$-$ Assume the user will enter an integer. However, if the number is out of range, display this message: "Invalid integer. Please try again."

$(3$c$)$ Store the code that calculates the number of factors for a number in its own function. $(8$ pts$.)$

$(3$d$)$ Store the rest of the code that gets input and displays output in the main$()$ function. If needed, divide this code into functions whenever you think it would make that code easier to read and maintain. $(10$ pts $.)$

$-$ The program should continue only if the user enters $"$y$"$ or $"$Y$"$ to continue.