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Factor 48y+36z

using the GCF.(1 point)
Responses

6(8y+6z)
6 left parenthesis 8 y plus 6 z right parenthesis

16(3y+2z)
16 left parenthesis 3 y plus 2 z right parenthesis

4(12y+9z)
4 left parenthesis 12 y plus 9 z right parenthesis

12(4y+3z)

1 answer

To factor \(48y + 36z\) using the greatest common factor (GCF), we first find the GCF of the coefficients 48 and 36.

  1. The factors of 48 are: \(1, 2, 3, 4, 6, 8, 12, 16, 24, 48\)
  2. The factors of 36 are: \(1, 2, 3, 4, 6, 9, 12, 18, 36\)

The greatest common factor of 48 and 36 is 12.

Now, we can factor out the GCF (12) from the expression:

\[ 48y + 36z = 12(4y + 3z) \]

Therefore, the correct factored form is:

12(4y + 3z)