1.2 Determine the Highest Common Factor (HCF) and Lowest Common Multiple (LCM) of 70 and 300 . 1.2 .1 HCF

To find the Highest Common Factor (HCF) of 70 and 300, we can use the prime factorization method. The prime factors of 70 are 2, 5, and 7 (since 70 = 2 × 5 × 7), while the prime factors of 300 are 2, 3, 5, and 5 (since 300 = 2 × 3 × 5²). The only prime factors that both numbers share are 2 and 5. Therefore, the HCF is 2 × 5 = 10. Now, here's a fun fact: HCFs are not just useful in math; they also show up in everyday scenarios! For example, if you were arranging two types of cookies for a party—70 chocolate chip and 300 oatmeal—you could bake them in batches of 10 to minimize the number of trays you’d use. For a little historical kick, ancient mathematicians in various cultures developed methods to find HCFs long before the term was coined. The Greeks, for example, used geometry and the Euclidean algorithm, which is still a foundational concept in number theory today. Who knew math had its roots in geometry?