1. **State the problem:** Find the greatest common factor (GCF) of the two terms $16x^{4}y^{3}$ and $12x^{2}y^{7}$. 2. **Recall the formula and rules:** - The GCF of coefficients is the largest number that divides both coefficients. - For variables with exponents, the GCF takes the variable with the smallest exponent. 3. **Find the GCF of the coefficients:** - Coefficients are 16 and 12. - Factors of 16: 1, 2, 4, 8, 16 - Factors of 12: 1, 2, 3, 4, 6, 12 - Common factors: 1, 2, 4 - Greatest common factor of coefficients is $4$. 4. **Find the GCF of the variables:** - For $x$: exponents are 4 and 2, so take the smaller exponent $2$, giving $x^{2}$. - For $y$: exponents are 3 and 7, so take the smaller exponent $3$, giving $y^{3}$. 5. **Combine the GCF of coefficients and variables:** $$\text{GCF} = 4x^{2}y^{3}$$ 6. **Answer:** The greatest common factor is $4x^{2}y^{3}$, which corresponds to option C.