Write an overloaded method that displays the prime factors of a positive integer in descending order. For example,

Argument Value Display

100 5 5 2 2

17 17

111 37 3

3960 11 5 3 3 2 2 2

Use the following method headers:

public static void showFactors(int number) private static void showFactors(int number, int factor) 

The public method showFactors() should call the private method showFactors(), with a value of 2 for the second parameter. So the public method should be written like the following example:

public static void showFactors(int number) { showFactors(number, 2); } 

The overloaded method effectively gives a default value of 2 for the second argument.

The private method showFactors() that you write must be recursive. You will not receive any credit for this lab for a solution that does not use recursion.

Do not use any loops in the methods that you write. Do not use any arrays or private data members in the methods that you write.

Write a driver program to test your methods. Submit your entire program, along with a capture of a sample run that includes the values listed above. Remember to provide documentation for your methods.

Sample dialog (user input in bold):

Enter a number, and I will display its prime factors in descending order

(enter 0 to exit program): 100

The factors for 100: 5 5 2 2

Enter a number, and I will display its prime factors in descending order

(enter 0 to exit program): 17

The factors for 17: 17

Enter a number, and I will display its prime factors in descending order

(enter 0 to exit program): 111

The factors for 111: 37 3

Enter a number, and I will display its prime factors in descending order

(enter 0 to exit program): 3960

The factors for 3960: 11 5 3 3 2 2 2

Enter a number, and I will display its prime factors in descending order

(enter 0 to exit program): 0

Goodbye!

Lab hints:

• Base case: number is 1
• Factor 100:

number factor

100 2

50 2

25 2

25 3

25 4

25 5

5 5

1

• Is a factor logic -- a number f is a factor of another number n if the remainder of n / f is zero. You can use the % operator to find a division's remainder.
• Use two different recursive calls:

if remainder is zero

try factor again

else

add one to factor

try factor again