Not including the factor provided, find two numbers less than 20 that have: \( \begin{array}{ll}\text { a } \text { an HCF of } 2 & \text { b an HCF of } 6\end{array} \)

To find two numbers less than 20 with the specified highest common factors (HCF), we can follow these steps: ### a) Two numbers with an HCF of 2 To have an HCF of 2, both numbers must be even, and they should not share any other common factors besides 2. Let's consider two even numbers less than 20: - 4 and 6: HCF(4, 6) = 2 (not valid since they share 2 and 2) - 4 and 8: HCF(4, 8) = 4 (not valid) - 4 and 10: HCF(4, 10) = 2 (valid) - 6 and 10: HCF(6, 10) = 2 (valid) - 8 and 10: HCF(8, 10) = 2 (valid) So, valid pairs with an HCF of 2 include: - (4, 10) - (6, 10) - (8, 10) ### b) Two numbers with an HCF of 6 To have an HCF of 6, both numbers must be multiples of 6, and they should not share any other common factors besides 6. The multiples of 6 that are less than 20 are: - 6 - 12 - 18 Now, we can check pairs: - (6, 12): HCF(6, 12) = 6 (valid) - (6, 18): HCF(6, 18) = 6 (valid) - (12, 18): HCF(12, 18) = 6 (valid) So, valid pairs with an HCF of 6 include: - (6, 12) - (6, 18) - (12, 18) ### Summary of Results - For HCF of 2: (4, 10), (6, 10), (8, 10) - For HCF of 6: (6, 12), (6, 18), (12, 18)