To find the Highest Common Factor (HCF) of 12 and 66, we can use the prime factorization method or the Euclidean algorithm. I'll use the Euclidean algorithm here.

### Euclidean Algorithm Steps:

1. **Divide the larger number by the smaller number and find the remainder.**
2. **Replace the larger number with the smaller number and the smaller number with the remainder.**
3. **Repeat this process until the remainder is 0.**
4. **The divisor at this step is the HCF.**

Let's apply these steps:

1. Divide 66 by 12:
   \[
   66 \div 12 = 5 \text{ remainder } 6 \quad (\text{since } 66 = 12 \times 5 + 6)
   \]

2. Replace 66 with 12 and 12 with 6. Now divide 12 by 6:
   \[
   12 \div 6 = 2 \text{ remainder } 0 \quad (\text{since } 12 = 6 \times 2 + 0)
   \]

3. The remainder is now 0, so the divisor at this step is the HCF.

Therefore, the HCF of 12 and 66 is **6**.

Would you like more details or have any questions? 

Here are 5 questions you might want to ask next:
1. What is the LCM of 12 and 66?
2. How do you find the HCF of three numbers?
3. Can you explain the prime factorization method for finding the HCF?
4. How is the Euclidean algorithm used to find the LCM?
5. What are the properties of the HCF?

**Tip:** The Euclidean algorithm is an efficient method for finding the HCF of two numbers, especially for larger numbers.

Learn how to find the Highest Common Factor (HCF) of 12 and 66 using the Euclidean algorithm. This method involves dividing the larger number by the smaller number and repeating until the remainder is 0. Follow a detailed step-by-step solution suitable for Grades 6-8.

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