1. Use Euclid's division algorithm to find the HCF of:

**(i) 135 and 225 (ii) 196 and 38220 (iii) 867 and 255**

(i) 135 and 225

To use **Euclid's division algorithm**, we apply **Euclid's division lemma** to given numbers **c and d,** to find whole numbers **q and r** such that

Here,

Remainder is not equal to 0. Therefore, we apply the same process again on 135 and 90

Remainder is not equal to 0 again. Therefore, we apply same process again on 90 and 45.

Remainder is equal to 0.

**Therefore, HCF of 135 and 225 is equal to 45 **which is equal to value of d in the last step**.**

(ii) 196 and 38220

To use **Euclid's division algorithm**, we apply **Euclid's division lemma** to given numbers **c and d**, to find whole numbers **q and r** such that

Here,

Remainder is equal to 0.

**Therefore, HCF of 196 and 38220 is equal to 196 **which is equal to value of d in the last step**.**

(iii) 867 and 255

To use **Euclid's division algorithm**, we apply **Euclid's division lemma** to given numbers **c and d,** to find whole numbers **q and r** such that

Here,

Remainder is not equal to 0. Therefore, we apply the same process again on 255 and 102

Remainder is not equal to 0 again. Therefore, we apply same process again on 102 and 51.

Remainder is equal to 0.

**Therefore, HCF of 867 and 255 is equal to 51 **which is equal to value of d in the last step**.**