1: Use Euclid’s division algorithm to find the HCF of: i. 135 and 225 ii. 196 and 38220 iii. 867 and 225 Answers: i. 135 and 225 As you can see, from the question 225 is greater than 135. Therefore, by Euclid’s division algorithm, we have, 225 = 135 × 1 + 90 Now, remainder 90 ≠ 0, thus again using division lemma for 90, we get, 135 = 90 × 1 + 45 Again, 45 ≠ 0, repeating the above step for 45, we get, 90 = 45 × 2 + 0 The remainder is now zero, so our method stops here. Since, in the last step, the divisor is 45, therefore, HCF (225,135) = HCF (135, 90) = HCF (90, 45) = 45. Hence, the HCF of 225 and 135 is 45. ii. 196 and 38220 In this given question, 38220>196, therefore the by applying Euclid’s division algorithm and taking 38220 as divisor, we get, 38220 = 196 × 195 + 0 We have already got the remainder as 0 here. Therefore, HCF(196, 38220) = 196. Hence, the HCF of 196 and 38220 is 196. iii. 867 and 225 As we know, 867 is greater ...
