1. The problem is to find the Highest Common Factor (HCF) of 196 and 144. 2. List the prime factors of each number. - Prime factors of 196: $$196 = 2^2 \times 7^2$$ - Prime factors of 144: $$144 = 2^4 \times 3^2$$ 3. Identify the common prime factors. - Common prime factor is $$2$$. 4. Take the lowest power of common prime factors. - Lowest power of 2 is $$2^2$$. 5. Calculate the HCF by multiplying the common prime factors with their lowest powers. $$\text{HCF} = 2^2 = 4$$ 6. Therefore, the HCF of 196 and 144 is $$4$$.