1. **State the problem:** Find the Highest Common Factor (HCF) of $196n^2$ and $144$. 2. **Prime factorize the numerical coefficients:** - $196 = 14^2 = (2 \times 7)^2 = 2^2 \times 7^2$ - $144 = 12^2 = (2^2 \times 3)^2 = 2^4 \times 3^2$ 3. **Include the variable factor in the factorization:** - $196n^2 = 2^2 \times 7^2 \times n^2$ - $144 = 2^4 \times 3^2$ 4. **Find the common prime factors with their lowest powers:** - For $2$: minimum power is $2$ - For $7$: no common factor in 144, so exclude - For $3$: no common factor in 196n², so exclude - For $n$: present only in $196n^2$, so exclude 5. **Calculate the HCF by multiplying common factors:** $$ \mathrm{HCF} = 2^2 = 4 $$ **Final answer:** The HCF of $196n^2$ and $144$ is $4$.