Question

Simpify 165/198

Answer 1

To simplify the fraction \( \frac{165}{198} \), we need to find the greatest common divisor (GCD) of the numerator and the denominator.

1. Find the prime factorization of 165:
- 165 = 3 × 5 × 11

2. Find the prime factorization of 198:
- 198 = 2 × 3 × 33
- 33 = 3 × 11, so 198 = 2 × 3² × 11

3. The common prime factors are \( 3 \) and \( 11 \).
4. 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 \( \frac{5}{6} \).