To find the Highest Common Factor (HCF) of 36 and 243, let's begin with their prime factorizations:

1. **Prime factorization:**
   - \( 36 = 2^2 \times 3^2 \)
   - \( 243 = 3^5 \)

2. **Common factors:**
   - The only common prime factor between 36 and 243 is \( 3 \).

3. **Finding the HCF:**
   - The lowest power of the common prime factor \( 3 \) is \( 3^2 \) (as it appears in both numbers).

So, the HCF of 36 and 243 is \( 3^2 = 9 \).

**The HCF of 36 and 243 is 9.**

Would you like more details or have any questions?

Here are some related questions you might find interesting:

1. What is the LCM of 36 and 243?
2. How can the Euclidean algorithm be applied to find the HCF of 36 and 243?
3. What are the steps to find the HCF of three or more numbers?
4. How do you determine the HCF if one number is a factor of the other?
5. What is the significance of the HCF in simplifying fractions?
6. Can the HCF be found using a Venn diagram?
7. What are the HCF and LCM of 36, 243, and another number?
8. How can the HCF be used to solve problems involving ratios?

**Tip:** The HCF of two numbers is the largest number that divides both numbers exactly. It's useful for simplifying fractions and solving problems related to divisibility.

Learn how to find the Highest Common Factor (HCF) of 36 and 243 using prime factorization and basic number theory concepts. Understand the method to determine common factors and compute the HCF efficiently. Suitable for students in Grades 7-9.

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