Question

4.3.1 gcd program. refer to the gcd code above. assume user input of numa = 15 and numb = 10. 1) for the gcd program, what is the value of numa before the first loop iteration? 2) what is the value of numb after the first iteration of the while loop? 3) what is numb after the second iteration of the while loop?

Explanation:

Step1: Recall GCD algorithm basics

The Euclidean algorithm for GCD typically involves replacing the larger number with the remainder of the division of the larger number by the smaller number in each loop iteration. Given numA = 15 and numB = 10 initially.

Step2: First loop iteration

In the first iteration of the loop for finding GCD, we divide 15 by 10. The remainder of 15 % 10 is 5. Then numA (the larger - number initially) is updated. But we are asked for numB after the first iteration. Since in the Euclidean algorithm, we swap values such that numA becomes the remainder and numB takes the value of the previous numA. So numB after the first iteration is 5.

Step3: Second loop iteration

Now, in the second iteration, we consider the new values. The new numA is 5 and new numB is 5. When we perform the operation for GCD (divide the larger by the smaller, in this case 5 % 5 = 0). After the second iteration, numB remains 5 because the algorithm terminates when the remainder is 0 and in this case, the values are equal and no further update to numB occurs in a non - terminating sense for the loop operation.

Answer:

1. 15
2. 5
3. 5