To find the greatest common divisor (gcd) of 27 and 12 using the provided function, we can apply the Euclidean algorithm.
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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, \( 27 \mod 12 = 3 \).
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Now we apply the gcd function:
- \( \text{gcd}(27, 12) = \text{gcd}(12, 3) \).
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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, \( 12 \mod 3 = 0 \).
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Now we apply the gcd function again:
- \( \text{gcd}(12, 3) = \text{gcd}(3, 0) \).
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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