(3 points)

Use Greatest Common Factor to rewrite the expression:

(63+81)
=
(
+
)

1 answer

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.