What is the output of the greatest common divisor function gcd(27,12) ? gcd(x,y)={x,gcd(y,x%y),y=0y>0 where x%y is remainder division or modulo (1 point) Responses 1 1 3 3 27 27 12
The output of the greatest common divisor function gcd(27,12) is 3.
To determine the output of the greatest common divisor (gcd) function gcd(27, 12), we can follow the step-by-step process described in the question.
Step 1: Start with the initial values:
x = 27
y = 12
Step 2: Check if y is zero. In this case, it is not zero, so we proceed to the next step.
Step 3: Calculate x%y, which represents the remainder of the division x/y:
x%y = 27%12 = 3
Step 4: Replace x with the value of y, and y with the value of x%y:
x = 12
y = 3
Step 5: Repeat steps 2 to 4 until y becomes zero:
x%y = 12%3 = 0
Since y is now zero, we stop the calculation.
The output of the gcd(27, 12) function is the value of x, which is 3.
Therefore, the output of gcd(27, 12) is 3.
To find the output of the greatest common divisor (gcd) function gcd(27,12), we can simply follow the definition given: gcd(x,y)={x,gcd(y,x%y),y=0y>0.
Starting with x=27 and y=12:
1. Since y=0 is not true, we move on to the next step.
2. Calculate x % y (remainder when x is divided by y): 27 % 12 = 3.
3. Now we update the values: x = y (12) and y = x % y (3).
4. Again, y is not 0, so we continue.
5. Calculate x % y: 12 % 3 = 0.
6. Now y is 0, which satisfies the condition to stop the recursive process.
7. Therefore, the gcd(27, 12) is the last non-zero remainder obtained, which is 3.
Hence, the output of the gcd(27, 12) function is 3.