One of the first algorithms written in a book is known as the Euclidean algorithm. It...

 

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One of the first algorithms written in a book is known as the Euclidean algorithm. It describes a method for finding the Greatest Common Divisor (GCD) of two positive integers. The GCD of two integers can help to reduce a fraction to a proper form (for example, 9/12 reduces to 3/4). In school you likely learned another method called factorization to do this that is, you factored the two integers and then reduced the fraction by crossing out common terms. Description of GCD Euclidean Algorithm 1. Start with two positive integers. 2. Replace the larger integer with the difference of the two integers. 3. Repeat the second step until the two integers are the same (this value is the GCD). Example of Euclidean Algorithm (18, 6)-> (12, 6)-> (6, 6) Detailed remarks: Initial pair of values: (18, 6) LOOP: next step, replace the larger value, 18, with (186) or 12 resulting in (12, 6) LOOP: next step, replace the larger value, 12, with (126) or 6 resulting in (6, 6) LOOP: stop the loop since the two values in the pair (6, 6) are the same. Therefore, the GCD of (18, 6) is 6. Write a C++ program that asks the user to enter a fraction (HINT: checkpoint 3.5). The program should implement the GCD algorithm described above to then reduce the fraction. The output of the program should show the original fraction, the reduced fraction and the computed GCD. Show the following three test cases with your screen shots: 3 / 12 1386 / 3213 105 / 252 One of the first algorithms written in a book is known as the Euclidean algorithm. It describes a method for finding the Greatest Common Divisor (GCD) of two positive integers. The GCD of two integers can help to reduce a fraction to a proper form (for example, 9/12 reduces to 3/4). In school you likely learned another method called factorization to do this that is, you factored the two integers and then reduced the fraction by crossing out common terms. Description of GCD Euclidean Algorithm 1. Start with two positive integers. 2. Replace the larger integer with the difference of the two integers. 3. Repeat the second step until the two integers are the same (this value is the GCD). Example of Euclidean Algorithm (18, 6)-> (12, 6)-> (6, 6) Detailed remarks: Initial pair of values: (18, 6) LOOP: next step, replace the larger value, 18, with (186) or 12 resulting in (12, 6) LOOP: next step, replace the larger value, 12, with (126) or 6 resulting in (6, 6) LOOP: stop the loop since the two values in the pair (6, 6) are the same. Therefore, the GCD of (18, 6) is 6. Write a C++ program that asks the user to enter a fraction (HINT: checkpoint 3.5). The program should implement the GCD algorithm described above to then reduce the fraction. The output of the program should show the original fraction, the reduced fraction and the computed GCD. Show the following three test cases with your screen shots: 3 / 12 1386 / 3213 105 / 252

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