What is the output of the greatest common divisor function gcd(27,12) ?

Question

gcd(x,y)={x,gcd(y,x%y),y=0y>0 where x%y is remainder division or modulo

(1 point)
Responses

12
12

3
3

27
27

1

Answer 1

To find the greatest common divisor (gcd) of 27 and 12 using the provided function, we can apply the Euclidean algorithm.

1. First, we calculate \( 27 \mod 12 \):

   • \( 27 \div 12 = 2 \) (which gives us a quotient of 2)
   • \( 2 \times 12 = 24 \)
   • \( 27 - 24 = 3 \)
   • Thus, \( 27 \mod 12 = 3 \).

2. Now we apply the gcd function:

   • \( \text{gcd}(27, 12) = \text{gcd}(12, 3) \).

3. Next, we calculate \( 12 \mod 3 \):

   • \( 12 \div 3 = 4 \) (which gives us a quotient of 4)
   • \( 4 \times 3 = 12 \)
   • \( 12 - 12 = 0 \)
   • Thus, \( 12 \mod 3 = 0 \).

4. Now we apply the gcd function again:

   • \( \text{gcd}(12, 3) = \text{gcd}(3, 0) \).

5. The gcd of any number and 0 is that number itself:

   • \( \text{gcd}(3, 0) = 3 \).

Thus, the output of \( \text{gcd}(27, 12) \) is 3.

The correct response is: 3