Write a recursive function (Java) called Fac which takes one positive integer argument (n) and returns n! You may not use a built-in factorial method or function.

1. Write a recursive method expFive(n) to compute y=5^n. For instance, if n is 0, y is 1. If n is 3, then y is 125. If n is 4, then y is 625. The recursive method cannot have loops. Then write a testing program to call the recursive method. If you run your program, the results should look like this: > run RecExpTest Enter a number: 3 125 >run RecExpTest Enter a number: 3125 2. For two integers m and n, their GCD(Greatest Common Divisor) can be computed by a recursive function. Write a recursive method gcd(m,n) to find their Greatest Common Divisor. Once m is 0, the function returns n. Once n is 0, the function returns m. If neither is 0, the function can recursively calculate the Greatest Common Divisor with two smaller parameters: One is n, the second one is m mod n. Although there are other approaches to calculate Greatest Common Divisor, please follow the instructions in this question, otherwise you will not get the credit. Meaning your code needs to follow the given algorithm. Then…

// The language is java Part I: Use of recursive method (4 points for students who need recursion/extracredit) Description: Code a class called RecursiveMultiply in which it will accept two integer arguments entered from user; pass these integers to a recursive method that returns the multiplication result of these two integers. The multiplication can be performed as repeated addition, for example, if two integers are 7 and 4: 8 * 4 = 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 You will write the application with GUI and recursion to display the result in a noneditable text field, based on the user’s entry from two text fields, while an OK button is pressed. You will utilize the exception handling code as you did in your Lab 4 and Lab 5 to verify if data entered in the text fields are valid (numerical and positive data only). You will make your own decision if there is any explanation that is not described in this specification. Finally, code a driver program that will test your class…

Lab Goal : This lab was designed to teach you more about recursion. Lab Description : Take a number and recursively determine how many of its digits are even. Return the count of the even digits in each number. % might prove useful to take the number apart digit by digit Sample Data : 453211145322224532714246813579 Sample Output : 23540