Project Documentation

Author: Matthew Festa

Problem-Solving Lifecycle:

1. Describe the problem:

This program will take the user input of two positive integers and determine the least common multiple (LCM) and the greatest common factor (GCF) of the two numbers. In addition, the program must determine if either number is a prime number or if either number is a ‘perfect’ number and output the above information to the user.

Four methods will be used to achieve the goals of the program.

A method that takes two positive integers as input and returns the least common multiple. The least common multiple of two positive integers (a, b) is the smallest positive integer that is perfectly divisible by both a and b.
A method that takes two positive integers as input and returns the greatest common factor. The greatest common factor of two positive integers (a, b) is the largest positive integer that can divide evenly into both a and b.
A method that takes a single integer as input and returns a true/false flag. If the number is prime, the method should return true, otherwise it should return false. A prime number is a positive integer greater than 1, that has only 2 factors, 1 and the number itself.
A method that takes a single integer as input and returns a true/false flag. If the number is ‘perfect’, the method should return true, otherwise it should return false. A ‘perfect’ number is a positive integer that is equal to the sum of its positive divisors, excluding the number itself.

The program output should look like this:

Example 1: Enter the first positive integer: 5 Enter the second positive integer: 6 The least common multiple (LCM) of 5 and 6 is: 30 The greatest common factor (GCF) of 5 and 6 is: 1 5 is a prime number. 6 is NOT a prime number. 5 is NOT a perfect number. 6 is a perfect number.

Example 2: (Looping until both numbers positive) Enter the first positive integer: -9 Enter the second positive integer: 54 Enter the first positive integer: 9 Enter the second positive integer: -54 Enter the first positive integer: 9 Enter the second positive integer: 54 The least common multiple (LCM) of 9 and 54 is: 54 The greatest common factor (GCF) of 9 and 54 is: 9 9 is NOT a prime number. 54 is NOT a prime number. 9 is NOT a perfect number. 54 is NOT a perfect number.

Example 3: Enter the first positive integer: 7 Enter the second positive integer: 11 The least common multiple (LCM) of 7 and 11 is: 77 The greatest common factor (GCF) of 7 and 11 is: 1 7 is a prime number. 11 is a prime number. 7 is NOT a perfect number. 11 is NOT a perfect number.

2. Analyze the problem:

a. What are the inputs? i. The first positive integer (a). ii. The second positive integer (b).

b. What are the outputs that should made by the solution to the problem? i. If a negative integer is entered, the program will loop until the number is positive.
ii. The first output will be the least common multiple (LCM) of the first and second positive integers. iii. The second output will be the greatest common factor (GCF) of the first and second positive integers. iv. The next output will determine if either integer is a prime number. v. The last output will determine if either integer is a perfect number.

c. How are the inputs and outputs related? i. The least common multiple (LCM) of two positive integers (a, b) is the smallest positive integer that is perfectly divisible by both a and b.
ii. The greatest common factor of two positive integers (a, b) is the largest positive integer that can divide evenly into both a and b. iii. A prime number is a positive integer greater than 1, that has only 2 factors, 1 and the number itself. iv. A ‘perfect’ number is a positive integer that is equal to the sum of its positive divisors, excluding the number itself.

d. Are there any constraints on the input? i. The integers must be non-negative integers. ii. If negative integers are inputted, they will be looped until they reach their positive integer equivalents.

3. Design the algorithm to solve the problem

  a. Prompt user for the first integer (a).
        1. If integer is negative, loop the input until its positive integer
        equivalent is reached. 
  b. Prompt user for the second integer (b).
        1. If integer is negative, loop the input until its positive integer
        equivalent is reached. 
  c. In the least common multiple method (int): loop through the multiples of both 
    integers (a) and (b) until the smallest possible integer that is perfectly
    disivisble by (a) and (b), the LCM.
        1. Return the LCM.
  d. In the greatest common factor method (int): loop through the factors of both 
    integers (a) and (b) until the largest possible integer that can divide
    evenly into both (a) and (b), the GCF.
        1. Return the GCF.
  e. In the prime number method (boolean): loop through to check if the number is 
    divisible by any number in the given range. If integer a or 
    b is divisible, the isPrime flag is set to false, and we break out of the
    loop. If a or b isn't divisible by any number, flag is true and num is a 
    prime number. 
        1. If input a is (not) a prime number, output that it is (not) 
        a prime number.
        2. If input b is (not) a prime number, output that it is (not) 
        a prime number.
  g. In the perfect number method (boolean): loop through the factors of 
    integer a and b and add them.  If the sum of all factors is the same as
    integer a or b, then the isPerfect flag is set to true and the number is
    perfect. If not, the flag is set to false and the number is not perfect. 
        1. If input a is (not) a perfect number, output that it is (not) a perfect number.
        2. If input b is (not) a perfect number, output that it is (not) a perfect number.

4. Test the correctness of algorithm using a trace:

Integer One	Integer Two	Expected LCM	Tested LCM	Expected GCF	Tested GCF	Expected Prime	Tested Prime	Expected Perfect	Tested Perfect
2	4	4	4	2	2	2: true / 4: false	2: true / 4: false	2: false / 4: false	2: false / 4: false
5	6	30	30	1	1	5: true / 6: false	5: true / 6: false	5: false / 6: true	5: false / 6: true
9	54	54	54	9	9	9: false / 54: false	9: false / 54: false	9: false / 54 false	9: false / 54 false
7	11	77	77	1	1	7: true / 11: true	7: true / 11: true	7: false / 11: false	7: false / 11: false
101	50	5050	5050	1	1	101: true / 50: false	101: true / 50: false	101: false / 50: false	101: false / 50: false
27	14	378	378	1	1	27: false / 14: false	27 false / 14: false	27: false / 14: false	27: false / 14: false
1985	1987	3944195	3944195	1	1	1985: false / 1987 true	1985: false / 1987 true	1985: false / 1987 false	1985: false / 1987 false
15	17	255	255	1	1	15: false / 17: true	15: false / 17: true	15: false / 17: false	15: false / 17: false
22	30	330	330	2	2	22: false / 30: false	22: false / 30: false	22: false / 30: false	22: false / 30: false
12	21	84	84	3	3	21: false / 12: false	21: false / 12: false	21: false / 12: false	21: false / 12: false

matthewfesta / IntegerCalcs