CBSE Class 10-Mathematics: Chapter – 8 Introduction to Trigonometry Part 15 (For CBSE, ICSE, IAS, NET, NRA 2022)

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Question6:

Use Euclid՚s division algorithm to find the HCF of:

(i) and

(ii) and

(iii) and

Answer:

(i) and

We have ,

So, we apply the division lemma to and to obtain

Here remainder , we apply the division lemma again to and to obtain

We consider the new divisor and new remainder , and apply the division lemma to obtain

Since that time, the remainder is zero, the process get stops.

The divisor at this stage is

Therefore, the HCF of and is .

(ii) and

and

We have ,

So, we apply the division lemma to and to obtain

Since we get the remainder is zero, the process stops.

The divisor at this stage is ,

Therefore, HCF of and is .

(iii) and

We have ,

So, we apply the division lemma to and to obtain

Here remainder , we apply the division lemma again to and to obtain

Here remainder , we apply the division lemma again to and to obtain

Since we get the remainder is zero, the process stops.

The divisor at this stage is ,

Therefore, HCF of and is .