The problem is to simplify the fraction $\frac{27}{63}$.

1. Problem Description

The problem is to simplify the fraction $\frac{27}{63}$.

2. Solution Steps

To simplify the fraction $\frac{27}{63}$, we need to find the greatest common divisor (GCD) of the numerator (27) and the denominator (63).

First, find the prime factorization of 27:

$27 = 3 \times 3 \times 3 = 3^3$

Next, find the prime factorization of 63:

$63 = 3 \times 3 \times 7 = 3^2 \times 7$

Now, find the GCD of 27 and

6

3. The common factors are $3 \times 3 = 3^2 = 9$.

So, GCD(27, 63) =

9.

Divide both the numerator and the denominator by their GCD, which is 9:

$\frac{27}{9} = 3$

$\frac{63}{9} = 7$

Therefore, the simplified fraction is $\frac{3}{7}$.

3. Final Answer

$\frac{3}{7}$