Question

(3 points)
Use Greatest Common Factor to rewrite the expression:

(63+81)
=
(
+
)

Answer 1

To rewrite the expression \( (63 + 81) \) using the Greatest Common Factor (GCF), we first need to determine the GCF of 63 and 81.

1. **Find the prime factorizations**:
- \( 63 = 3^2 \times 7 \)
- \( 81 = 3^4 \)

2. **Identify the common factors**:
The only common prime factor is \( 3 \). The lowest power of \( 3 \) that appears in both factorizations is \( 3^2 \).

3. **Calculate the GCF**:
Thus, the GCF of 63 and 81 is \( 9 \) (since \( 3^2 = 9 \)).

4. **Factor out the GCF**:
Now, we can express both numbers in terms of the GCF:
- \( 63 = 9 \times 7 \)
- \( 81 = 9 \times 9 \)

5. **Rewrite the expression**:
Therefore, we can rewrite \( (63 + 81) \) as:
\[
(63 + 81) = (9 \times 7 + 9 \times 9) = 9(7 + 9)
\]

Putting it all together, we have:

\[
(63 + 81) = (9)(7 + 9)
\]

So the final expression becomes:
\[
9(7 + 9)
\]

This is the rewritten form using the Greatest Common Factor.