Question

Simplify 1287 ÷ 1225

Answer 1

To simplify \( 1287 \div 1225 \), we start by finding the greatest common divisor (GCD) of the two numbers.

The prime factorization of 1225 is:
\[
1225 = 35 \times 35 = 5^2 \times 7^2.
\]

For 1287, we can check for divisibility by prime numbers:

- Check divisibility by 3:
\[
1 + 2 + 8 + 7 = 18 \quad (\text{which is divisible by } 3).
\]
So, divide 1287 by 3:
\[
1287 \div 3 = 429.
\]

Now we factor 429:
- Check divisibility by 3 again:
\[
4 + 2 + 9 = 15 \quad (\text{which is divisible by } 3).
\]
So, divide 429 by 3:
\[
429 \div 3 = 143.
\]

Next, we factor 143:
- Check for divisibility by 11:
\[
1 - 4 + 3 = 0 \quad (\text{so, } 143 \text{ is divisible by } 11).
\]
Thus,
\[
143 \div 11 = 13.
\]

So, the prime factorization of 1287 is:
\[
1287 = 3^2 \times 11 \times 13.
\]

Now, let's summarize the factorizations:
- \( 1287 = 3^2 \times 11 \times 13 \)
- \( 1225 = 5^2 \times 7^2 \)

Since there are no common factors between \( 1287 \) and \( 1225 \), we can conclude that the GCD is 1, which means the fraction \( \frac{1287}{1225} \) is in its simplest form.

Thus,
\[
1287 \div 1225 = \frac{1287}{1225}
\]
is already simplified and does not further reduce. The answer can be presented as the fraction:

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

If you prefer a decimal representation, you can calculate:

\[
\frac{1287}{1225} \approx 1.0502.
\]

So, the simplified form is \(\frac{1287}{1225}\) or approximately \(1.0502\).