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