2. The highest common factor (HCF) of 60 and 144 is equal to: A 144 B. 60 C. 720 D. 12

To find the highest common factor (HCF) of 60 and 144, we start by finding the prime factors. The prime factorization of 60 is 2^2 × 3 × 5, while for 144 it is 2^4 × 3^2. The common prime factors are 2 and 3. Taking the lowest powers of these factors gives us 2^2 (which is 4) and 3^1 (which is 3). Therefore, HCF = 4 × 3 = 12. The correct answer is D. 12! For a bit of historical background, the concept of factors goes way back to ancient civilizations where numbers were crucial, particularly to the Greeks. They explored number theory extensively and contributed to our understanding of how numbers interact, including factors and multiples. This mathematical foundation has been built upon over centuries, leading us to modern techniques for finding HCFs. In practical terms, knowing how to find the HCF is super helpful! It's often used in simplifying fractions, where it can help you reduce them to their simplest form. For example, if you're baking and you want to halve a recipe, finding the HCF of the ingredients can ensure you measure the right amounts without waste. It's a handy little tool in the kitchen and beyond!