The **highest common factor (HCF)**, also known as the greatest common divisor (GCD), of 900 and 3375 can be calculated using their prime factorizations:

1. **Prime factorization of 900:**
   \[
   900 = 2^2 \times 3^2 \times 5^2
   \]

2. **Prime factorization of 3375:**
   \[
   3375 = 3^3 \times 5^3
   \]

Now, the HCF is determined by taking the lowest power of each common prime factor.

- For 3: The lowest power is \( 3^2 \).
- For 5: The lowest power is \( 5^2 \).

Therefore, the HCF is:
\[
\text{HCF} = 3^2 \times 5^2 = 9 \times 25 = 225
\]

Thus, the HCF of 900 and 3375 is **225**.

Would you like more details on the process, or have any further questions?

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Here are five related questions to deepen your understanding:

1. How do you find the prime factorization of a number?
2. What is the difference between HCF and LCM?
3. Can the HCF of two numbers ever be larger than either number?
4. How do you apply the Euclidean algorithm to find the HCF?
5. What is the relationship between HCF and the prime factors of numbers?

**Tip:** The Euclidean algorithm is a quick method to find the HCF of large numbers!

Learn how to find the highest common factor (HCF) of 900 and 3375 using prime factorization. This solution involves breaking down each number into its prime factors and applying the HCF formula. Suitable for students in Grades 6-8.

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