Simplify the following fraction: \( \frac{36}{99} \)

To simplify the fraction \( \frac{36}{99} \), we need to find the greatest common divisor (GCD) of the numerator (36) and the denominator (99). First, we can find the prime factorization of both numbers: - The prime factorization of 36 is: \[ 36 = 2^2 \times 3^2 \] - The prime factorization of 99 is: \[ 99 = 3^2 \times 11 \] Next, we identify the common factors. The only common prime factor is \( 3 \), and the lowest power of \( 3 \) in both factorizations is \( 3^2 \). Thus, the GCD of 36 and 99 is: \[ GCD(36, 99) = 3^2 = 9 \] Now, we can simplify the fraction by dividing both the numerator and the denominator by their GCD (9): \[ \frac{36 \div 9}{99 \div 9} = \frac{4}{11} \] Therefore, the simplified form of the fraction \( \frac{36}{99} \) is: \[ \boxed{\frac{4}{11}} \]