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Factor 48y+36z using the GCF.(1 point)

Responses

12(4y+3z)
12 left parenthesis 4 y plus 3 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

6(8y+6z)

1 answer

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.

  1. Finding the GCF:

    • The factors of 48: \( 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 \)
    • The factors of 36: \( 1, 2, 3, 4, 6, 9, 12, 18, 36 \)
    • The common factors: \( 1, 2, 3, 4, 6, 12 \)
    • The greatest of these is \( 12 \).

  2. Factoring out the GCF: Now we divide each term by the GCF (which is 12): \[ 48y \div 12 = 4y \] \[ 36z \div 12 = 3z \]

  3. Writing the factored form: Therefore, the expression can be factored as: \[ 48y + 36z = 12(4y + 3z) \]

So, the correct factored form is:

12(4y + 3z)