To factor the expression \( 48y + 36z \) using the greatest common factor (GCF), we first need to find the GCF of the coefficients 48 and 36.
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Find the GCF of 48 and 36:
- The factors of 48 are: \( 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 \)
- The factors of 36 are: \( 1, 2, 3, 4, 6, 9, 12, 18, 36 \)
- The common factors are: \( 1, 2, 3, 4, 6, 12 \)
- The greatest of these is \( 12 \).
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Factor out the GCF:
- We can rewrite the expression as follows: \[ 48y + 36z = 12(4y + 3z) \]
Therefore, the factored form of \( 48y + 36z \) using the GCF is: \[ 12(4y + 3z) \]
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