To factor the expression \(16d - 12\) using the greatest common factor (GCF), we first need to identify the GCF of the coefficients 16 and 12.
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Find the GCF of 16 and 12:
- The factors of 16 are: \(1, 2, 4, 8, 16\)
- The factors of 12 are: \(1, 2, 3, 4, 6, 12\)
- The common factors are: \(1, 2, 4\)
- The greatest of these is \(4\).
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Factor out the GCF from the expression: \[ 16d - 12 = 4(4d) - 4(3) \] \[ = 4(4d - 3) \]
Therefore, the factored form of \(16d - 12\) using the GCF is: \[ \boxed{4(4d - 3)} \]