1. Find the highest common factor (HCF) of $12x^{12}$ and $16x^{16}$. The HCF of two terms is found by taking the HCF of the coefficients and the lowest power of common variables. 2. Coefficients: HCF of 12 and 16. Prime factors of 12: $2^2 \times 3$ Prime factors of 16: $2^4$ HCF of coefficients = $2^2 = 4$ 3. Variables: Take the lowest power of $x$ common to both terms. Lowest power of $x$ is $x^{12}$. 4. Therefore, HCF = $4x^{12}$. Final answer: $4x^{12}$.