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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 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 \( 9 \).

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

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

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

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

  3. 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:

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