To simplify the fraction \( \frac{165}{198} \), we need to find the greatest common divisor (GCD) of the numerator and the denominator.
-
Find the prime factorization of 165:
- 165 = 3 × 5 × 11
-
Find the prime factorization of 198:
- 198 = 2 × 3 × 33
- 33 = 3 × 11, so 198 = 2 × 3² × 11
-
The common prime factors are \( 3 \) and \( 11 \).
-
The GCD is \( 3 × 11 = 33 \).
Now, divide both the numerator and the denominator by their GCD:
\[ \frac{165 \div 33}{198 \div 33} = \frac{5}{6} \]
Therefore, the simplified form of \( \frac{165}{198} \) is \( \frac{5}{6} \).