To find the greatest common factor (GCF) of the expressions [tex]\(4y^2\)[/tex] and [tex]\(7w^4\)[/tex], we need to consider both the numerical coefficients and the variable parts separately.
1. Finding the GCF of the Coefficients:
- The coefficients in the expressions are [tex]\(4\)[/tex] and [tex]\(7\)[/tex].
- We need to find the greatest common factor of these two numbers.
- The factors of [tex]\(4\)[/tex] are [tex]\(1, 2, 4\)[/tex].
- The factors of [tex]\(7\)[/tex] are [tex]\(1, 7\)[/tex].
- The only common factor is [tex]\(1\)[/tex], so the GCF of the coefficients [tex]\(4\)[/tex] and [tex]\(7\)[/tex] is [tex]\(1\)[/tex].
2. Finding the GCF of the Variable Parts:
- The first expression has the variable part [tex]\( y^2 \)[/tex].
- The second expression has the variable part [tex]\( w^4 \)[/tex].
- Since the variables [tex]\(y\)[/tex] and [tex]\(w\)[/tex] are different, there is no common variable factor. Hence, the GCF of the variable parts is [tex]\(1\)[/tex].
Combining these results:
- The GCF of the coefficients is [tex]\(1\)[/tex].
- The GCF of the variable parts is also [tex]\(1\)[/tex].
[tex]\[
\text{Therefore, the GCF of } 4y^2 \text{ and } 7w^4 \text{ is } 1.
\][/tex]
