To find the highest common factor (HCF) of 244 and 644, we can use the Euclidean algorithm. The Euclidean algorithm involves repeated division to find the greatest common divisor (GCD), which is the same as the HCF.

### Steps:
1. Divide 644 by 244 and find the remainder.
2. Divide 244 by the remainder obtained in step 1.
3. Repeat the process until the remainder is 0. The divisor at this stage is the HCF.

Let's calculate:

1. \( 644 \div 244 = 2 \) remainder \( 156 \)
2. \( 244 \div 156 = 1 \) remainder \( 88 \)
3. \( 156 \div 88 = 1 \) remainder \( 68 \)
4. \( 88 \div 68 = 1 \) remainder \( 20 \)
5. \( 68 \div 20 = 3 \) remainder \( 8 \)
6. \( 20 \div 8 = 2 \) remainder \( 4 \)
7. \( 8 \div 4 = 2 \) remainder \( 0 \)

Since the remainder is now 0, the divisor at this stage is 4. 

### Therefore, the HCF of 244 and 644 is **4**.

Would you like to go through the detailed steps again or need any further explanation?

Here are 5 related questions you might find interesting:
1. How do you find the least common multiple (LCM) of 244 and 644?
2. What is the relationship between the HCF and LCM of two numbers?
3. How can you use prime factorization to find the HCF?
4. What is the HCF of 244, 644, and 1244?
5. How do you find the HCF of two numbers using their prime factors?

**Tip:** The Euclidean algorithm is a powerful method for finding the HCF, especially with larger numbers, as it reduces the problem step by step efficiently.

Learn how to find the Highest Common Factor (HCF) of 244 and 644 using the Euclidean Algorithm. This step-by-step solution covers the number theory concept of greatest common divisor (GCD) and provides an easy-to-follow method for students in Grades 6-8.

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