To find the Highest Common Factor (HCF) of 3556 and 3444, we'll follow these steps:

1. **List the factors** of each number.
2. **Identify the common factors**.
3. **Choose the highest** of those common factors.

However, a more efficient method is to use the **Euclidean algorithm**. Here's how it works:

### Step 1: Apply the Euclidean Algorithm

1. **Divide the larger number by the smaller number**, and find the remainder.
2. **Replace the larger number** with the smaller number and the smaller number with the remainder.
3. Repeat this process until the remainder is 0. The divisor at this stage will be the HCF.

Let's calculate:

1. \( 3556 \div 3444 \) gives a quotient of 1 and a remainder of \( 3556 - 3444 = 112 \).
2. Now, apply the algorithm to 3444 and 112:
   \[
   3444 \div 112 \approx 30 \text{ with a remainder of } 3444 - (112 \times 30) = 84
   \]
3. Apply the algorithm to 112 and 84:
   \[
   112 \div 84 \approx 1 \text{ with a remainder of } 112 - 84 = 28
   \]
4. Apply the algorithm to 84 and 28:
   \[
   84 \div 28 = 3 \text{ with a remainder of } 0
   \]

Since the remainder is now 0, the HCF is **28**.

### The HCF of 3556 and 3444 is 28.

Would you like any more details or have any questions?

Here are 8 related questions for further exploration:

1. How do you find the HCF using prime factorization?
2. What is the difference between HCF and Least Common Multiple (LCM)?
3. Can you find the LCM of 3556 and 3444?
4. How would you calculate the HCF of three or more numbers?
5. What is the significance of the Euclidean algorithm in number theory?
6. How do you find the HCF of two numbers that are coprime?
7. Can the HCF of two numbers ever be larger than the smaller number?
8. How does the HCF relate to simplifying fractions?

**Tip:** The Euclidean algorithm is a powerful and efficient way to find the HCF, especially with large numbers!

Discover how to find the Highest Common Factor (HCF) of 3556 and 3444 using the Euclidean algorithm. Follow a step-by-step explanation with calculations and understand the significance of the Euclidean algorithm in number theory. Suitable for high school students and anyone interested in number theory and algorithms.

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