Find the HCF of the following pairs of numbers: 155 and 1385

Introduction

In this problem, we will find the Highest Common Factor (HCF) of the numbers 155 and 1385. 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: 155 and 1385.

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 1385 by 155.

1385 = 155 × 8 + 145

Step 2: Now divide 155 by 145.

155 = 145 × 1 + 10

Step 3: Now divide 145 by 10.

145 = 10 × 14 + 5

Step 4: Now divide 10 by 5.

10 = 5 × 2 + 0

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

Therefore, the HCF of 155 and 1385 is 5.

Conclusion

Hence, using Euclid’s Division Algorithm, we find that the Highest Common Factor (HCF) of 155 and 1385 is 5.

Hence proved.