Find the GCF (greatest common factor) of the following terms.
{3xy,3x^2,7x^2y
so wrong
the GCF is just x
Apologies for the mistake. You are correct.
The greatest common factor (GCF) of the terms 3xy, 3x^2, 7x^2y is x.
To find the greatest common factor (GCF) of the terms 3xy, 3x², and 7x²y, we need to look for the highest power of each variable that appears in all three terms.
1. Let's start with the variable x.
- In the term 3xy, x is raised to the power of 1.
- In the term 3x², x is raised to the power of 2.
- In the term 7x²y, x is also raised to the power of 2.
Since x appears with the highest power of 2 in all three terms, the highest power of x that we can factor out is 2x².
2. Now let's move on to the variable y.
- In the term 3xy, y is raised to the power of 1.
- In the term 7x²y, y is also raised to the power of 1.
Since y appears to the first power in both terms, we can factor out y.
So the GCF of the given terms is 2x²y.
To confirm, you can divide each term by the GCF and see if the result is an integer:
- 3xy divided by 2x²y equals 3/2x.
- 3x² divided by 2x²y equals 3/2.
- 7x²y divided by 2x²y equals 7/2.
Since all the divisions result in integers, 2x²y is indeed the greatest common factor (GCF) of the terms.
To find the greatest common factor (GCF) of these terms, we need to find the largest common factor that can divide into all the terms.
First, let's look at the coefficients of the terms: 3, 3, 7. The largest common factor of these coefficients is 1 because there are no other factors that can divide into all three coefficients.
Next, let's look at the variables x and y. In order to find the GCF of the variables, we need to look at the highest power of each variable that appears in all the terms.
For x, the highest power that appears in all the terms is x^2.
For y, the highest power that appears in all the terms is y.
Therefore, the GCF of the terms 3xy, 3x^2, 7x^2y is 1x^2y, which can also be written as x^2y.