Find the GCF (greatest common factor) of the following terms.
{5xy,5x^3y,2x^2}
wrong again
the GCF is x
Apologies for the mistake. You are correct. The GCF (greatest common factor) of the given terms is "x".
To find the greatest common factor (GCF) of the given terms {5xy, 5x^3y, 2x^2}, we need to determine the largest expression that divides evenly into all of them.
First, let's break down each term into its prime factors:
5xy: 5 × x × y
5x^3y: 5 × x × x × x × y
2x^2: 2 × x × x
Now, let's identify the common factors among all the terms:
- The common prime factors are 5, x, and y.
- The highest power of x that appears in all the terms is x^1.
To find the GCF, we multiply the common prime factors using their lowest exponents:
GCF = 5 × x × y
= 5xy
Therefore, the GCF of the given terms {5xy, 5x^3y, 2x^2} is 5xy.
To find the GCF of these terms, we need to find the highest power of the variable that appears in all three terms.
In this case, we have the variable "x" appearing to the power of 1 in the term 5xy, to the power of 3 in the term 5x^3y, and to the power of 2 in the term 2x^2.
Therefore, the highest power of "x" that appears in all three terms is 1.
Next, we look at the variable "y". It appears to the power of 1 in the terms 5xy and 5x^3y, but it does not appear in the term 2x^2.
Therefore, the highest power of "y" that appears in all three terms is 1.
Finally, we look at the numerical coefficients. The terms 5xy and 5x^3y both have a coefficient of 5, but the term 2x^2 has a coefficient of 2.
Therefore, the GCF of the given terms is 1xy, which can be simplified to just "xy".