To find the highest common factor (HCF) of 24, 60, and 90, we can use the prime factorization method.

1. **Prime factorization of each number:**
   - \( 24 = 2^3 \times 3 \)
   - \( 60 = 2^2 \times 3 \times 5 \)
   - \( 90 = 2 \times 3^2 \times 5 \)

2. **Identify the common prime factors with the lowest powers:**
   - The common prime factors are \( 2 \) and \( 3 \).
   - For \( 2 \), the lowest power among the numbers is \( 2^1 \).
   - For \( 3 \), the lowest power among the numbers is \( 3^1 \).

3. **Multiply the common factors:**
   \[
   \text{HCF} = 2^1 \times 3^1 = 2 \times 3 = 6
   \]

**The HCF of 24, 60, and 90 is 6.**

Would you like more details or have any questions?

Here are some related questions for further exploration:
1. How do we find the HCF of larger numbers efficiently?
2. What is the relationship between HCF and LCM?
3. Can you find the HCF of other sets of three numbers?
4. How does the HCF differ from the greatest common divisor (GCD)?
5. Why is it useful to find the HCF in real-life situations?

**Tip:** Prime factorization is a useful method for both finding the HCF and simplifying fractions.

Learn how to find the highest common factor (HCF) of 24, 60, and 90 using the prime factorization method. This solution breaks down the prime factorizations of each number and identifies the common factors to find the HCF, which is 6. Perfect for students in Grades 6-8.

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