To simplify \( 1287 \div 1225 \), we start by finding the greatest common divisor (GCD) of the two numbers.
The prime factorization of 1225 is: \[ 1225 = 35 \times 35 = 5^2 \times 7^2. \]
For 1287, we can check for divisibility by prime numbers:
- Check divisibility by 3: \[ 1 + 2 + 8 + 7 = 18 \quad (\text{which is divisible by } 3). \] So, divide 1287 by 3: \[ 1287 \div 3 = 429. \]
Now we factor 429:
- Check divisibility by 3 again: \[ 4 + 2 + 9 = 15 \quad (\text{which is divisible by } 3). \] So, divide 429 by 3: \[ 429 \div 3 = 143. \]
Next, we factor 143:
- Check for divisibility by 11: \[ 1 - 4 + 3 = 0 \quad (\text{so, } 143 \text{ is divisible by } 11). \] Thus, \[ 143 \div 11 = 13. \]
So, the prime factorization of 1287 is: \[ 1287 = 3^2 \times 11 \times 13. \]
Now, let's summarize the factorizations:
- \( 1287 = 3^2 \times 11 \times 13 \)
- \( 1225 = 5^2 \times 7^2 \)
Since there are no common factors between \( 1287 \) and \( 1225 \), we can conclude that the GCD is 1, which means the fraction \( \frac{1287}{1225} \) is in its simplest form.
Thus, \[ 1287 \div 1225 = \frac{1287}{1225} \] is already simplified and does not further reduce. The answer can be presented as the fraction:
\[ \frac{1287}{1225} \]
If you prefer a decimal representation, you can calculate:
\[ \frac{1287}{1225} \approx 1.0502. \]
So, the simplified form is \(\frac{1287}{1225}\) or approximately \(1.0502\).
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