To simplify \( 1287 \div 1225 \), we can start by simplifying the fraction:
\[ \frac{1287}{1225} \]
First, we look for the greatest common divisor (GCD) of 1287 and 1225.
Step 1: Factor both numbers.
- The prime factorization of 1225:
\[ 1225 = 35 \times 35 = 5^2 \times 7^2 \]
- The prime factorization of 1287 involves checking for divisibility:
\[ 1287 \div 3 = 429 \quad (\text{since } 1 + 2 + 8 + 7 = 18 \text{ is divisible by } 3) \] Next, we factor 429:
\[ 429 \div 3 = 143 \] Then, factor 143:
\[ 143 = 11 \times 13 \]
Thus, the prime factorization of 1287 is:
\[ 1287 = 3^2 \times 11 \times 13 \]
Step 2: The GCD and simplify the fraction.
The prime factors we have found are:
- For 1287: \(3^2 \times 11 \times 13\)
- For 1225: \(5^2 \times 7^2\)
There are no common factors between the two numbers. Thus, the GCD is \(1\).
Step 3: Simplify the fraction.
Since the GCD is \(1\), we cannot simplify the fraction further:
\[ \frac{1287}{1225} \text{ remains as it is.} \]
Step 4: Convert to decimal.
To calculate the decimal value, we can perform the division:
\[ 1287 \div 1225 \approx 1.05 \]
So, the simplified answer to \( 1287 \div 1225 \) is:
\[ \frac{1287}{1225} \text{ or approximately } 1.05 \]