To find the greatest common factor (GCF) of the given expressions [tex]\(16x^4y^3\)[/tex] and [tex]\(12x^2y^7\)[/tex], you need to follow these steps:
1. Identify the coefficients of each term:
- From [tex]\(16x^4y^3\)[/tex], the coefficient is 16.
- From [tex]\(12x^2y^7\)[/tex], the coefficient is 12.
2. Find the GCF of the coefficients:
- The factors of 16 are [tex]\(1, 2, 4, 8, 16\)[/tex].
- The factors of 12 are [tex]\(1, 2, 3, 4, 6, 12\)[/tex].
- The greatest common factor of 16 and 12 is 4.
3. Identify the variables and their respective exponents:
- In [tex]\(16x^4y^3\)[/tex], the variables are [tex]\(x^4\)[/tex] and [tex]\(y^3\)[/tex].
- In [tex]\(12x^2y^7\)[/tex], the variables are [tex]\(x^2\)[/tex] and [tex]\(y^7\)[/tex].
4. Find the GCF of the variable parts:
- For [tex]\(x^4\)[/tex] and [tex]\(x^2\)[/tex], the GCF is [tex]\(x^{\min(4, 2)} = x^2\)[/tex].
- For [tex]\(y^3\)[/tex] and [tex]\(y^7\)[/tex], the GCF is [tex]\(y^{\min(3, 7)} = y^3\)[/tex].
5. Combine the GCF of the coefficients and the variables:
- The GCF of the coefficients is 4.
- The GCF of the variable parts [tex]\(x^4\)[/tex] and [tex]\(x^2\)[/tex] is [tex]\(x^2\)[/tex].
- The GCF of the variable parts [tex]\(y^3\)[/tex] and [tex]\(y^7\)[/tex] is [tex]\(y^3\)[/tex].
Putting it all together, the greatest common factor of [tex]\(16x^4y^3\)[/tex] and [tex]\(12x^2y^7\)[/tex] is:
[tex]\[4x^2y^3\][/tex]
Thus, the correct answer is:
[tex]\[ \boxed{4x^2y^3} \][/tex]
