To simplify \( \frac{1287}{1225} \), we can look for the greatest common divisor (GCD) of 1287 and 1225.
First, we can factor both numbers:
For 1287:
- Check divisibility by 3 (sum of digits is 18, which is divisible by 3): \[ 1287 \div 3 = 429 \]
- Now, check 429. Sum of digits is 15, which is also divisible by 3: \[ 429 \div 3 = 143 \]
- Now factor 143. It is \( 11 \times 13 \).
So, the factorization of 1287 is: \[ 1287 = 3^2 \times 11 \times 13 \]
For 1225:
- Check if 1225 is a perfect square (it ends with 25). It is \( 35^2 \): \[ 1225 = 25 \times 49 = 5^2 \times 7^2 \]
Thus, \( 1225 = 5^2 \times 7^2 \).
Finding GCD: The GCD of 1287 and 1225 is 1 since they have no common prime factors.
Therefore, the fraction \( \frac{1287}{1225} \) is already in simplest form.
So, the simplified result is: \[ \frac{1287}{1225} \]
You can also express it as a decimal: \[ 1287 \div 1225 \approx 1.05 \]
Thus the final answer can be presented as: \[ \frac{1287}{1225} \text{ or } 1.05 \]