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Data Structures and Algorithms Unit Test 14 of 2214 of 22 Items 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 1 1 3 3 12 12 27 27 Skip to navigation page 1 of 1

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To find the greatest common divisor (GCD) of the numbers 27 and 12 using the provided function, we use the formula:

  • gcd(x, y) = gcd(y, x % y) when \( y > 0 \)
  • gcd(x, 0) = x

We'll compute gcd(27, 12):

  1. Compute \( 27 % 12 = 3 \) (since 27 divided by 12 gives a quotient of 2 and a remainder of 3).
  2. Now, we compute gcd(12, 3).

Continuing the computation:

  1. Compute \( 12 % 3 = 0 \) (since 12 divided by 3 gives a quotient of 4 and a remainder of 0).
  2. Now, we have gcd(3, 0).

According to the rule, gcd(x, 0) = x, which means:

  • gcd(3, 0) = 3.

So, the output for gcd(27, 12) is 3.

Thus, the correct response is 3.