Find the HCF of the following pairs of numbers: 75 and 243

Introduction

In this problem, we are required to find the Highest Common Factor (HCF) of the numbers 75 and 243 using Euclid’s Division Algorithm.

Video Solution

Question

Find the HCF of the following pairs of numbers: 75 and 243.

Solution

We use Euclid’s Division Algorithm to find the HCF.

Step 1: Divide 243 by 75.

243 = 75 × 3 + 18

Step 2: Divide 75 by 18.

75 = 18 × 4 + 3

Step 3: Divide 18 by 3.

18 = 3 × 6 + 0

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

Therefore, the HCF of 75 and 243 is 3.

Conclusion

Hence, the Highest Common Factor (HCF) of the numbers 75 and 243 is 3.

Hence proved.