Question

Consider the following C code segment: 

The output of the given C code segment is __________. (Answer in integer)

Hint:

The given C code implements the Euclidean algorithm to compute the greatest common divisor (GCD) of two numbers.

Answer 1

This code implements the Euclidean algorithm to compute the greatest common divisor (GCD) of \( x = 126 \) and \( y = 105 \). The Euclidean algorithm works by repeatedly subtracting the smaller number from the larger number until the two numbers become equal, at which point the common value is the GCD.

• Step 1: Start with \( x = 126 \) and \( y = 105 \).
• Step 2: Subtract \( y = 105 \) from \( x = 126 \), resulting in \( x = 21 \) and \( y = 105 \).
• Step 3: Subtract \( x = 21 \) from \( y = 105 \), resulting in \( x = 21 \) and \( y = 84 \).
• Step 4: Subtract \( x = 21 \) from \( y = 84 \), resulting in \( x = 21 \) and \( y = 63 \).
• Step 5: Subtract \( x = 21 \) from \( y = 63 \), resulting in \( x = 21 \) and \( y = 42 \).
• Step 6: Subtract \( x = 21 \) from \( y = 42 \), resulting in \( x = 21 \) and \( y = 21 \).
• Step 7: Since \( x = y = 21 \), the loop terminates, and the GCD is \( 21 \).

The final value, \( 21 \), is the greatest common divisor of \( 126 \) and \( 105 \), as determined by the Euclidean algorithm.