To find the greatest common factor (GCF) of the given terms [tex]\(4x y^2\)[/tex] and [tex]\(20x^2 y^4\)[/tex], follow these steps:
### Step 1: Find the GCF of the Coefficients
- The coefficients are 4 and 20.
- We need to find the greatest common factor of these numbers.
- The divisors of 4 are: 1, 2, 4.
- The divisors of 20 are: 1, 2, 4, 5, 10, 20.
- The common divisors are 1, 2, and 4.
- Thus, the greatest common factor of 4 and 20 is 4.
### Step 2: Find the GCF of the Variables
- For the variable [tex]\(x\)[/tex]:
- The first term has [tex]\(x^1\)[/tex], and the second term has [tex]\(x^2\)[/tex].
- The least power of [tex]\(x\)[/tex] common to both is [tex]\(x^1\)[/tex].
- For the variable [tex]\(y\)[/tex]:
- The first term has [tex]\(y^2\)[/tex], and the second term has [tex]\(y^4\)[/tex].
- The least power of [tex]\(y\)[/tex] common to both is [tex]\(y^2\)[/tex].
### Step 3: Combine the Results
- Combine the GCF of the coefficients with the GCF of the variable terms.
Thus, the GCF of [tex]\(4x y^2\)[/tex] and [tex]\(20x^2 y^4\)[/tex] is:
[tex]\[ 4 \cdot x^1 \cdot y^2 = 4 x y^2 \][/tex]
### Conclusion
The greatest common factor of [tex]\(4x y^2\)[/tex] and [tex]\(20x^2 y^4\)[/tex] is [tex]\(4 x y^2\)[/tex].
Thus, the correct answer is:
[tex]\[ 4 x y^2 \][/tex]
