Find the HCF of the following pairs of numbers: 32 and 54

Introduction

In this problem, we are required to find the Highest Common Factor (HCF) of the numbers 32 and 54. We will use Euclid’s Division Algorithm to find the HCF.

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Question

Find the HCF of the following pairs of numbers: 32 and 54.

Solution

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

Step 1: Divide 54 by 32.

54 = 32 × 1 + 22

Step 2: Divide 32 by 22.

32 = 22 × 1 + 10

Step 3: Divide 22 by 10.

22 = 10 × 2 + 2

Step 4: Divide 10 by 2.

10 = 2 × 5 + 0

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

Therefore, the HCF of 32 and 54 is 2.

Conclusion

Hence, the Highest Common Factor (HCF) of the numbers 32 and 54 is 2.

Hence proved.