Use properties of operations to factor 16x+28y+32z using the GCF.
A. 8(2x + 3y + 4z)
B. 2(8x + 14y +16z)
C. 6(10x + 22y =26z)
D. 4(4x + 7y + 8z)
To factor by using the greatest common factor (GCF), we first need to identify the GCF of the coefficients of the terms 16x, 28y, and 32z.
The coefficients are 16, 28, and 32. Let's determine their GCF:
- The prime factorization of 16 is 2 x 2 x 2 x 2.
- The prime factorization of 28 is 2 x 2 x 7.
- The prime factorization of 32 is 2 x 2 x 2 x 2 x 2.
The common factors in each prime factorization are 2 x 2, which means the GCF is 4 (because 2 x 2 = 4).
Now we can divide each term by the GCF of 4 to factor out the expression:
16x / 4 = 4x
28y / 4 = 7y
32z / 4 = 8z
Thus, the factored expression using the GCF is:
4(4x + 7y + 8z)
The correct answer is:
D. 4(4x + 7y + 8z)