To find the Highest Common Factor (HCF) of 27, 63, and 207, we can use the prime factorization method.

Step 1: Prime Factorization

1. Prime factorization of 27: $27 = 3 \times 3 \times 3 = 3^3$

2. Prime factorization of 63: $63 = 3 \times 3 \times 7 = 3^2 \times 7$

3. Prime factorization of 207: $207 = 3 \times 3 \times 23 = 3^2 \times 23$

Step 2: Identify the Common Factors

• The common prime factor among 27, 63, and 207 is $3$.

Step 3: Select the Lowest Power of the Common Factor

• The lowest power of $3$ common to all three numbers is $3^2$.

Step 4: Calculate the HCF

• The HCF is $3^2 = 9$.

Thus, the HCF of 27, 63, and 207 is 9.

Do you want more details, or do you have any questions?

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Here are some related questions you might be interested in:

1. How do you find the HCF of two numbers using the division method?
2. What is the least common multiple (LCM) of 27, 63, and 207?
3. How can the HCF be used to simplify fractions?
4. What is the relationship between HCF and GCD (Greatest Common Divisor)?
5. How do you find the HCF of more than two numbers?
6. How can you verify the HCF using the Euclidean algorithm?
7. What are some practical applications of HCF in problem-solving?
8. How do you find the LCM of three numbers and relate it to the HCF?

Tip: When dealing with multiple numbers, start by finding the HCF of two numbers first, then use that result to find the HCF with the third number.