To simplify the fraction \( \frac{1287}{1225} \), we can start by finding the greatest common divisor (GCD) of the two numbers.
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Prime Factorization:
- For \( 1225 \):
- \( 1225 = 35 \times 35 = 5^2 \times 7^2 \)
- For \( 1287 \):
- \( 1287 \div 3 = 429 \)
- \( 429 \div 3 = 143 \)
- \( 143 = 11 \times 13 \)
- So, \( 1287 = 3^2 \times 11 \times 13 \)
- For \( 1225 \):
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GCD:
- The prime factors of \( 1287 \) ( \( 3, 11, 13 \) ) and \( 1225 \) ( \( 5, 7 \) ) do not share any common factors.
- Thus, the GCD is 1.
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Simplified Fraction: Since the GCD is 1, we cannot simplify the fraction further. Therefore:
\[ \frac{1287}{1225} \text{ is already in its simplest form.} \]
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Approximate Decimal Value: If you need a decimal approximation:
\[ 1287 \div 1225 \approx 1.050 \]
So, in summary, \( \frac{1287}{1225} \) is already simplified and has a decimal approximation of about 1.050.