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# Use Euclid’s division algorithm to find the HCF of:

**(i)** 135 and 225.

**(ii)** 196 and 38220.

**(iii)** 867 and 255.

Given:

(i) 135 and 225.

(ii) 196 and 38220.

(iii) 867 and 255.

To find:

Here we have to find the HCF of the given numbers.

Solution:

Using Euclid's division algorithm to find HCF:

(i) Using Euclid’s lemma to get:

- $225\ =\ 135\ \times\ 1\ +\ 90$

Now, consider the divisor 135 and the remainder 90, and apply the division lemma to get:

- $135\ =\ 90\ \times\ 1\ +\ 45$

Now, consider the divisor 90 and the remainder 45, and apply the division lemma to get:

- $90\ =\ 45\ \times\ 2\ +\ 0$

The remainder has become zero, and we cannot proceed any further.

Therefore the HCF of 225 and 135 is the divisor at this stage, i.e., 45.

So, HCF of 135 and 225 is 45.

(ii) Using Euclid’s lemma to get:

- $38220\ =\ 196\ \times\ 195\ +\ 0$

The remainder has become zero, and we cannot proceed any further.

Therefore the HCF of 38220 and 196 is the divisor at this stage, i.e., 196.

So, HCF of 196 and 38220 is 196.

(iii) Using Euclid’s lemma to get:

- $867\ =\ 255\ \times\ 3\ +\ 102$

Now, consider the divisor 255 and the remainder 102, and apply the division lemma to get:

- $255\ =\ 102\ \times\ 2\ +\ 51$

Now, consider the divisor 102 and the remainder 51, and apply the division lemma to get:

- $102\ =\ 51\ \times\ 2\ +\ 0$

The remainder has become zero, and we cannot proceed any further.

Therefore the HCF of 867 and 255 is the divisor at this stage, i.e., 51.

So, HCF of 867 and 255 is 51.

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