Use Euclid’s Division Algorithm to find the HCF of 196 and 38220

Introduction

In this problem, we will find the Highest Common Factor (HCF) of the numbers 196 and 38220. Let us solve it step by step using Euclid’s Division Algorithm, just like a teacher explains the method in class.

Video Solution

Question

Use Euclid’s Division Algorithm to find the HCF of 196 and 38220.

Solution

According to Euclid’s Division Algorithm, we divide the larger number by the smaller number and then divide the divisor by the remainder. We repeat this process until the remainder becomes zero.

Step 1: Divide 38220 by 196.

38220 = 196 × 195 + 0

Since the remainder has become zero in the first step itself, the divisor 196 is the HCF of the given numbers.

Therefore, the HCF of 196 and 38220 is 196.

Conclusion

Hence, using Euclid’s Division Algorithm, we find that the Highest Common Factor (HCF) of 196 and 38220 is 196.

Hence proved.