To rewrite the expression \( (63 + 81) \) using the Greatest Common Factor (GCF), we first need to determine the GCF of 63 and 81.
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Find the prime factorizations:
- \( 63 = 3^2 \times 7 \)
- \( 81 = 3^4 \)
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Identify the common factors: The only common prime factor is \( 3 \). The lowest power of \( 3 \) that appears in both factorizations is \( 3^2 \).
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Calculate the GCF: Thus, the GCF of 63 and 81 is \( 9 \) (since \( 3^2 = 9 \)).
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Factor out the GCF: Now, we can express both numbers in terms of the GCF:
- \( 63 = 9 \times 7 \)
- \( 81 = 9 \times 9 \)
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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.