To simplify \( \frac{1287}{1225} \), we can look for the greatest common divisor (GCD) of 1287 and 1225.
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First, let's find the prime factorization of both numbers.
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1287:
- Start dividing by 3: \( 1287 \div 3 = 429 \)
- Divide 429 by 3: \( 429 \div 3 = 143 \)
- Now factor 143: \( 143 = 11 \times 13 \)
- So, \( 1287 = 3^2 \times 11 \times 13 \)
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1225:
- \( 1225 = 35 \times 35 = 5^2 \times 7^2 \)
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Now we have:
- \( 1287 = 3^2 \times 11 \times 13 \)
- \( 1225 = 5^2 \times 7^2 \)
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Since 1287 and 1225 have no common factors, the GCD is 1.
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Therefore, \( \frac{1287}{1225} \) is already in its simplest form.
The simplification of \( \frac{1287}{1225} \) is:
\[ \frac{1287}{1225} \text{ (already simplified)} \]