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