Factor 8a − 28 using the GCF.
To factor the expression 8a - 28 using the GCF (Greatest Common Factor), we need to find the largest number that divides evenly into both terms. Let's list the factors of both terms:
Factors of 8a: 1, 2, 4, 8, a, 2a, 4a, 8a
Factors of 28: 1, 2, 4, 7, 14, 28
The GCF is the largest common factor, which in this case is 4. We can now rewrite the expression as:
8a - 28 = 4(2a - 7)
So, the expression 8a - 28 can be factored as 4(2a - 7).
To factor 8a - 28 using the greatest common factor (GCF), let's first find the GCF of the two terms.
The GCF of 8 and 28 is 4 because it is the largest number that divides both 8 and 28 without leaving a remainder.
Now, let's factor out the GCF.
Factor out 4 from both terms:
8a can be written as 4 * 2 * a
28 can be written as 4 * 7
Now we can rewrite the original expression as:
8a - 28 = 4 * 2 * a - 4 * 7
When we factor out the GCF, we get:
8a - 28 = 4(2a - 7)
Therefore, the factored form of 8a - 28 using the GCF is 4(2a - 7).
To factor 8a - 28 using the Greatest Common Factor (GCF), we need to find the largest number or variable that divides evenly into both terms.
Let's begin by finding the GCF of 8a and 28. The GCF of two numbers involves finding the highest power of each common factor. In this case, we can break down 8a and 28 into their prime factorizations:
8a = 2 * 2 * 2 * a
28 = 2 * 2 * 7
Now, let's identify the common factors between the two terms:
Common factors: 2 * 2 = 4
The GCF is 4.
To factor out the GCF of 4, we divide both terms by 4:
8a / 4 = 2a
28 / 4 = 7
Therefore, the factored form of 8a - 28 using the GCF is:
4(2a - 7)