Find the HCF of the following pairs of numbers: 100 and 190

Introduction

In this problem, we will find the Highest Common Factor (HCF) of the numbers 100 and 190. 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: 100 and 190.

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 190 by 100.

190 = 100 × 1 + 90

Step 2: Now divide 100 by 90.

100 = 90 × 1 + 10

Step 3: Now divide 90 by 10.

90 = 10 × 9 + 0

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

Therefore, the HCF of 100 and 190 is 10.

Conclusion

Hence, using Euclid’s Division Algorithm, we find that the Highest Common Factor (HCF) of 100 and 190 is 10.

Hence proved.