What is the output of the greatest common divisor function gcd(27,12) ?%0D%0A%0D%0Agcd(x,y)={x,gcd(y,x%y),y=0y>0 where x%y is remainder division or modulo%0D%0A%0D%0A(1 point)%0D%0AResponses%0D%0A%0D%0A1%0D%0A1%0D%0A%0D%0A12%0D%0A12%0D%0A%0D%0A27%0D%0A27%0D%0A%0D%0A3
The output of the greatest common divisor function gcd(27,12) is 3.
To find the greatest common divisor (GCD) of two numbers, we can use the Euclidean algorithm. The Euclidean algorithm uses the property that the GCD of two numbers is equal to the GCD of the smaller number and the difference between the larger number and the smaller number.
Let's apply the Euclidean algorithm to find the GCD of 27 and 12:
1. Divide the larger number (27) by the smaller number (12) and find the remainder: 27 % 12 = 3
2. Now, we need to find the GCD of the smaller number (12) and the remainder (3). Repeat the same process:
- Divide the smaller number (12) by the remainder (3) and find the new remainder: 12 % 3 = 0
- Since the remainder is now 0, we stop the process.
3. The GCD is the last non-zero remainder. In this case, the GCD of 27 and 12 is 3.
So, the output of the greatest common divisor function gcd(27,12) is 3.
To find the greatest common divisor (gcd) of 27 and 12 using the gcd(x, y) function, we can follow these steps:
Step 1: Initialize x = 27 and y = 12.
Step 2: Calculate x % y (remainder of division): 27 % 12 = 3.
Step 3: Check if y is equal to 0. Since y is not equal to 0, we continue.
Step 4: Update x with the current value of y: x = 12.
Step 5: Update y with the current value of x % y: y = 3.
Step 6: Repeat steps 2-5 until y becomes 0.
- Calculate x % y: 12 % 3 = 0.
- Since y is now equal to 0, we stop the loop.
The gcd of 27 and 12 is the final non-zero value of y, which is 3.