Question

(3 points) Use Greatest Common Factor to rewrite the expression: (63+81) = ( + )

Answer 1

To find the expression for \( (63 + 81) \) using the greatest common factor (GCF), we first need to determine the GCF of 63 and 81.

1. **Prime factorization of the numbers:**
- \( 63 = 3^2 \times 7 \)
- \( 81 = 3^4 \)

2. **Identify the GCF:**
- The common factor here is \( 3 \). The smallest power of \( 3 \) in both factorizations is \( 3^2 = 9 \).

So, the GCF of 63 and 81 is 9.

3. **Rewrite the expression:**

Now, we can factor out the GCF from the original expression:

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

4. **Final expression:**

So, the rewritten expression is:

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

Thus, \( (63 + 81) = (9 \times 7) + (9 \times 9) \).