To simplify \( \frac{1287}{1225} \), we need to find the greatest common divisor (GCD) of 1287 and 1225 and then divide both the numerator and the denominator by that GCD.
First, we can factor both numbers:
- Finding the GCD:
- The prime factorization of 1287:
- \( 1287 = 3 \times 429 = 3 \times 3 \times 143 = 3^2 \times 11 \times 13 \)
- The prime factorization of 1225:
- \( 1225 = 25 \times 49 = 5^2 \times 7^2 \)
- The prime factorization of 1287:
Since there are no common prime factors, the GCD of 1287 and 1225 is 1. This means the fraction is already in its simplest form.
Therefore, \( \frac{1287}{1225} \) cannot be simplified further, and the simplified result is:
\[ \frac{1287}{1225} \]
If you want a decimal approximation, it is approximately \( 1.05 \). However, as a fraction, it remains \( \frac{1287}{1225} \).
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