Question

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 find the GCF of the numbers 63 and 81.

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

2. **Finding the GCF**:
The GCF is found by taking the lowest power of each common prime factor:
- The common prime factor is \( 3 \).
- The lowest power of \( 3 \) in the factorizations is \( 3^2 \) (which is \( 9 \)).

So, the GCF of \( 63 \) and \( 81 \) is \( 9 \).

3. **Rewriting the expression**:
Now, we express \( 63 \) and \( 81 \) in terms of the GCF:

- \( 63 = 9 \times 7 \)
- \( 81 = 9 \times 9 \)

4. **Factoring out the GCF**:
Now, we can factor out \( 9 \) from the expression:

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

5. **Simplifying further**:
Finally, calculate \( 7 + 9 \):

\[
7 + 9 = 16
\]

So, the expression can be rewritten as:

\[
63 + 81 = 9(16)
\]

Thus, the complete rewritten expression is:

\[
63 + 81 = 9(16)
\]