Determine the highest common factor of numerator and denominator

To determine the highest common factor (HCF), or greatest common divisor (GCD), of a fraction’s numerator and denominator, follow these steps:

1. **Identify the numerator and denominator**: For example, if the fraction is \( \frac{36}{48} \), the numerator is 36, and the denominator is 48.
  
2. **Prime factorization**: Find the prime factorization of both the numerator and denominator.
   - 36: \( 36 = 2^2 \times 3^2 \)
   - 48: \( 48 = 2^4 \times 3 \)

3. **Find the common factors**: Look for the common prime factors between the two numbers. In this case:
   - Both 36 and 48 share \( 2^2 \) and \( 3 \).

4. **Determine the highest common factor**: Multiply the common prime factors:
   - HCF = \( 2^2 \times 3 = 12 \)

So, the highest common factor of 36 and 48 is **12**.

Would you like details on a specific part or further explanation?

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Here are 5 related questions to consider:
1. How do you find the HCF of two numbers without prime factorization?
2. What is the difference between HCF and LCM (Least Common Multiple)?
3. Can the HCF of two numbers ever be larger than the smaller of the two numbers?
4. How do you simplify a fraction using the HCF?
5. What is the relationship between the GCD and the Euclidean algorithm?

**Tip**: The Euclidean algorithm is a quick method for finding the GCD of two numbers by repeatedly subtracting or dividing until reaching zero.

Learn how to find the highest common factor (HCF) of a fraction's numerator and denominator. This guide covers prime factorization, identifying common factors, and using the Euclidean algorithm to simplify fractions. Suitable for students in Grades 6-8.

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