To simplify \( \frac{1287}{1225} \), we can start by finding the greatest common divisor (GCD) of the two numbers.
First, we can factor both numbers:
-
Factoring \( 1287 \):
- Dividing by \( 3 \): \( 1287 \div 3 = 429 \)
- Dividing \( 429 \) by \( 3 \): \( 429 \div 3 = 143 \)
- Factoring \( 143 \): It's \( 11 \times 13 \).
- So, \( 1287 = 3^2 \times 11 \times 13 \).
-
Factoring \( 1225 \):
- \( 1225 = 35^2 = (5 \times 7)^2 = 5^2 \times 7^2 \).
Now we have:
- \( 1287 = 3^2 \times 11 \times 13 \)
- \( 1225 = 5^2 \times 7^2 \)
Since there are no common factors, the GCD is \( 1 \).
Thus, the fraction \( \frac{1287}{1225} \) is already in its simplest form.
Therefore, \( 1287 \div 1225 \) does not simplify further and the answer is:
\[ \frac{1287}{1225} \]
If you want it in decimal form, \( 1287 \div 1225 \approx 1.05 \).