Question

Simplify 1287÷1225
12
87
÷
12
25
.(1 point)

Answer 1

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:

\[
\frac{1287}{1225} \text{ or approximately } 1.05
\]