This image displays prime factor trees for the numbers 66 and 110. Let's calculate the Highest Common Factor (HCF) step by step.

Prime Factorization:

1. 66:

   • $66 = 2 \times 33$
   • $33 = 3 \times 11$
   • Prime factors: $2, 3, 11$

2. 110:

   • $110 = 2 \times 55$
   • $55 = 5 \times 11$
   • Prime factors: $2, 5, 11$

Common Prime Factors:

• Both 66 and 110 have the common factors $2$ and $11$.

HCF:

• Multiply the common factors: $HCF = 2 \times 11 = 22$

Final Answer:

The HCF of 66 and 110 is 22.

Do you need further explanation or examples? Here are 5 related questions for practice:

1. What is the LCM (Least Common Multiple) of 66 and 110?
2. Why is the HCF helpful when simplifying fractions like $\frac{66}{110}$?
3. How can you use the Euclidean algorithm to find the HCF?
4. What are the steps for constructing a prime factor tree for a number?
5. How do prime factors help in solving problems involving divisors and multiples?

Tip:

When working with prime factorization, always double-check by multiplying the factors back to ensure the number is correct.