Find the HCF of the following pairs of numbers: 475 and 495

Introduction

In this problem, we are required to find the Highest Common Factor (HCF) of the numbers 475 and 495 using Euclid’s Division Algorithm.

Video Solution

Question

Find the HCF of the following pairs of numbers: 475 and 495.

Solution

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

Step 1: Divide 495 by 475.

495 = 475 × 1 + 20

Step 2: Divide 475 by 20.

475 = 20 × 23 + 15

Step 3: Divide 20 by 15.

20 = 15 × 1 + 5

Step 4: Divide 15 by 5.

15 = 5 × 3 + 0

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

Therefore, the HCF of 475 and 495 is 5.

Conclusion

Hence, the Highest Common Factor (HCF) of the numbers 475 and 495 is 5.

Hence proved.