1. **State the problem:** Find the Highest Common Factor (HCF) of the numbers 36, 24, and 12. 2. **Prime factorize each number:** - $36 = 2^2 \times 3^2$ - $24 = 2^3 \times 3$ - $12 = 2^2 \times 3$ 3. **Identify the common prime factors with lowest powers:** - For $2$, the smallest power among 36, 24, and 12 is $2^2$. - For $3$, the smallest power among 36, 24, and 12 is $3^1$. 4. **Multiply these lowest powers to find the HCF:** $$HCF = 2^2 \times 3 = 4 \times 3 = 12$$ 5. **Conclusion:** The HCF of 36, 24, and 12 is $12$.