# . Use Euclids division algorithm to find the HCF of

(i) 135 and 225

(ii) 196 and 38220

(iii) 867 and 225

Explanation:

(i) 135 and 225

Since 225 > 135, apply the Euclid’s division lemma to 135 and 225, to get

225= 135 × 1+ 90

Since the remainder O, apply the division lemma to 135 and 90, to get

135=90 × 1+ 45

Now, consider the new divisor 90 and new reminder 45, and apply the division lemma to get

The remainder is zero.

So, the divisior at this stage is 45, the HCF of 1.35 and 225 is 45.

(ii) 196 and 38220

Since 38220 > 196, apply the Euclid's division lemma to 196 and 38220, to get

38220= 195+ o

The remainder is zero.

So, the divisior at this stage is 196, the HCF of 196 and 38220 is 196.

(iii) 867 and 225

Since 867 > 255, apply the Euclid's division lemma to 867 and 225, to get

867=255 × 3+ 102

Since the reminder 102* O, apply the division lemma to 102 and 225, to get

255= 2+ 51

Now, consider the new divisor 102 and the new reminder 51, and apply the division lemma to get

102=51 × 2+0

The remainder is zero.

So, the divisior at this stage is 51, the HCF of 867 and 225 is 51.

Final Answer. (i) HCF of 135 and 225 is 45.

(ii) HCF of 196 and 38220 is 196.

(iii) HCF of 867 and 225 is 51.