Question

Simplify 1287÷1225
.(1 point)
$$

Answer 1

To simplify the fraction \( \frac{1287}{1225} \), we can start by finding the greatest common divisor (GCD) of the two numbers.

First, we list the prime factorization of each number:

1. **Finding the prime factorization of 1225**:
- 1225 is \( 35 \times 35 \) (since \( 35^2 = 1225 \)).
- Further factor \( 35 = 5 \times 7 \).
- So, \( 1225 = 5^2 \times 7^2 \).

2. **Finding the prime factorization of 1287**:
- We can divide by 3 (sum of digits \( 1 + 2 + 8 + 7 = 18 \), which is divisible by 3):
\( 1287 \div 3 = 429 \).
- Next, we factor 429. The sum of the digits \( 4 + 2 + 9 = 15 \) is divisible by 3:
\( 429 \div 3 = 143 \).
- Finally, we factor 143. The factors of 143 are \( 11 \times 13 \) (since both 11 and 13 are prime numbers).

Now, we have:
\[
1287 = 3^2 \times 11 \times 13,
\]
\[
1225 = 5^2 \times 7^2.
\]

Now, since there are no common factors between \( 1287 \) (which has prime factors 3, 11, and 13) and \( 1225 \) (which has prime factors 5 and 7), the GCD is \( 1 \).

Thus, \( \frac{1287}{1225} \) is already in its simplest form. Therefore, the simplified form of \( 1287 \div 1225 \) is:

\[
\frac{1287}{1225}.
\]

There is no further simplification possible.