1. **State the problem:** We need to find the Highest Common Factor (HCF) of 144 and 96. 2. **Formula and rules:** The HCF of two numbers is the largest number that divides both without leaving a remainder. 3. **Method:** Use the Euclidean algorithm: - Divide the larger number by the smaller number. - Replace the larger number with the smaller number and the smaller number with the remainder. - Repeat until the remainder is 0. 4. **Step-by-step calculation:** - Divide 144 by 96: $$144 \div 96 = 1$$ remainder $$48$$ - Now find HCF of 96 and 48. - Divide 96 by 48: $$96 \div 48 = 2$$ remainder $$0$$ 5. **Conclusion:** When the remainder is 0, the divisor at this step is the HCF. **Final answer:** $$\boxed{48}$$