Find the HCF of the following pairs of numbers: 105 and 120

Introduction

In this problem, we will find the Highest Common Factor (HCF) of the numbers 105 and 120. Let us understand the solution step by step using Euclid’s Division Algorithm, just like a teacher explains in class.

Video Solution

Question

Find the HCF of the following pairs of numbers: 105 and 120.

Solution

Let us find the HCF using Euclid’s Division Algorithm. According to this method, we divide the larger number by the smaller number and continue the process until the remainder becomes zero.

Step 1: Divide 120 by 105.

120 = 105 × 1 + 15

Step 2: Now divide 105 by 15.

105 = 15 × 7 + 0

Since the remainder has become zero, the divisor at this stage is the HCF.

Therefore, the HCF of 105 and 120 is 15.

Conclusion

Hence, using Euclid’s Division Algorithm, we find that the Highest Common Factor (HCF) of 105 and 120 is 15.

Hence proved.