factor 16d - 12 using the GCF
To factor 16d - 12 using the GCF (Greatest Common Factor), we need to find the largest number or variable that can divide both 16d and 12.
First, let's find the GCF of 16d and 12.
The prime factorization of 16d: 2 * 2 * 2 * 2 * d
The prime factorization of 12: 2 * 2 * 3
The common factors of 16d and 12 are 2 (appears twice).
Therefore, the GCF of 16d and 12 is 2 * 2 = 4.
Now, we can factor out 4 from 16d - 12:
16d - 12 = 4(4d - 3)
So, the factored form of 16d - 12 using the GCF is 4(4d - 3).
Factor 9z + 18 using the GCF
To factor 9z + 18 using the GCF (Greatest Common Factor), we need to find the largest number or variable that can divide both 9z and 18.
First, let's find the GCF of 9z and 18.
The prime factorization of 9z: 3 * 3 * z
The prime factorization of 18: 2 * 3 * 3
The common factors of 9z and 18 are 3 and 3.
Therefore, the GCF of 9z and 18 is 3 * 3 = 9.
Now, we can factor out 9 from 9z + 18:
9z + 18 = 9(z + 2)
So, the factored form of 9z + 18 using the GCF is 9(z + 2).
To factor 16d - 12 using the greatest common factor (GCF), we first need to find the GCF of the terms 16d and 12.
Step 1: Find the GCF of 16d and 12.
The factors of 16d are 1, 2, 4, 8, 16, d, 2d, 4d, 8d, 16d.
The factors of 12 are 1, 2, 3, 4, 6, 12.
The common factors are 1, 2, and 4.
Therefore, the GCF of 16d and 12 is 4.
Step 2: Divide both terms by the GCF.
16d / 4 = 4d
12 / 4 = 3
Step 3: Rewrite the expression using the factored form.
The factored form of 16d - 12 using the GCF is:
4(4d - 3)
To factor the expression 16d - 12 using the GCF (Greatest Common Factor), we need to find the largest number or term that can be divided evenly into both 16d and 12.
Step 1: Find the GCF of the numerical coefficients (16 and 12).
The common factors of 16 are 1, 2, 4, 8, and 16.
The common factors of 12 are 1, 2, 3, 4, 6, and 12.
The largest number that can be divided evenly into both 16 and 12 is 4.
Step 2: Identify the GCF of the variable terms' exponents.
Since both 16d and 12 have a "d" term, we consider the variable portion.
Step 3: Write the factored expression using the GCF.
The GCF of 16d and 12 is 4, and since both terms have a "d" term, we can factor out "4d".
So, the factored expression is 4d(4 - 3).