. Find the HCF of a) 52 x 2 and 25 x 5 b) 4 and 44

Let's calculate the Highest Common Factor (HCF) for each part:

### a) HCF of \( 52 \times 2 \) and \( 25 \times 5 \):

1. \( 52 \times 2 = 104 \)
2. \( 25 \times 5 = 125 \)

To find the HCF of 104 and 125, we can use the prime factorization method:

- **Prime factorization of 104**:
  \[
  104 = 2^3 \times 13
  \]
- **Prime factorization of 125**:
  \[
  125 = 5^3
  \]

There are no common prime factors between 104 and 125, so the HCF is:

\[
\text{HCF} = 1
\]

### b) HCF of 4 and 44:

- **Prime factorization of 4**:
  \[
  4 = 2^2
  \]
- **Prime factorization of 44**:
  \[
  44 = 2^2 \times 11
  \]

The common prime factor is \( 2^2 \), so the HCF is:

\[
\text{HCF} = 4
\]

### Final Answers:
- (a) HCF = 1
- (b) HCF = 4

Would you like more details or explanations? Here are some follow-up questions:

1. How can you find HCF using the division method?
2. Why does the HCF of \( 104 \) and \( 125 \) result in 1?
3. Can the HCF of two numbers ever be greater than either of them?
4. How do you apply the Euclidean algorithm to find the HCF?
5. What are some real-world applications of finding HCF?

**Tip:** When two numbers have no common prime factors, their HCF will always be 1.

Find the HCF of a) 52 x 2 and 25 x 5 b) 4 and 44

Learn how to find the Highest Common Factor (HCF) for the numbers 104 and 125, and 4 and 44. This solution uses prime factorization and provides a step-by-step explanation, suitable for students in Grades 6-8.

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