Question

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

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**.