How to find HCF of 30 and 67 by using Euclid division lemma?

Academic Mathematics NCERT Class 10

Given: 30, 67

To find: We have to find the HCF of 30, 67 by using Euclid division lemma

Solution:

HCF of the integers 30 and 67.

Using Euclid’s lemma to get

67 = 30 $\times $ 2 $+$ 7

Now consider the divisor 30 and the remainder 5, and apply the division lemma to get

30 = 7 $\times $ 4 $+$ 2

Now consider the divisor 7 and the remainder 2, and apply the division lemma to get

7 = 2 $\times $ 3 $+$ 1

Now consider the divisor 2 and the remainder 1, and apply the division lemma to get

2 = 1 $\times $ 2 $+$ 0

Notice that the remainder has become zero, and we cannot proceed any further.

Therefore the HCF of 30 and 67 is the divisor at this stage, i.e., 1.

HCF (30, 67) = 1

Simply Easy Learning

Updated on: 10-Oct-2022

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