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

27
27

1
1

12
12

3

Answer 1

To find the greatest common divisor (gcd) of 27 and 12, we can use the Euclidean algorithm.

1. Start with \( x = 27 \) and \( y = 12 \).
2. Calculate \( x % y \): \[ 27 % 12 = 3 \]
3. Now, replace \( x \) with \( y \) and \( y \) with \( x % y \): \[ gcd(12, 3) \]
4. Again compute \( 12 % 3 \): \[ 12 % 3 = 0 \]
5. Now, replace again: \[ gcd(3, 0) \]
6. According to the definition, if \( y = 0 \), then \( gcd(x, 0) = x \). So: \[ gcd(3, 0) = 3 \]

Thus, \( gcd(27, 12) = 3 \).

The output of the greatest common divisor function \( gcd(27, 12) \) is 3.