Unit 1 Real Numbers Exercise 1.1, 1.2, 1.3, 1.4 Solutions Exercise 1.1 : Solutions of Questions on Page Number : 7 Q1 : Use Euclid’s division algorithm to find the HCF of: Answer : (i) 135 and 225 Since 225 > 135, we apply the division lemma to 225 and 135 to obtain 225 = 135 x 1 + 90 Since remainder 90 ≠ 0, we apply the division lemma to 135 and 90 to obtain 135 = 90 x 1 + 45 We consider the new divisor 90 and new remainder 45, and apply the division lemma to obtain 90 = 2 x 45 + 0 Since the remainder is zero, the process stops. Since the divisor at this stage is 45, Therefore, the HCF of 135 and 225 is 45. (ii)196 and 38220 Since 38220 > 196, we apply the division lemma to 38220 and 196 to obtain 38220 = 196 x 195 + 0 Since the remainder is zero, the process stops. Since the divisor at this stage is 196, Therefore, HCF of 196 and 38220 is 196. (iii)867 and 255 Since 867 > 255, we apply the division lemma to 867 and 255 to obtain 867 = 255 x 3 + 102 Since remainder 102 ≠ 0, we apply the division lemma to 255 and 102 to obtain 255 = 102 x 2 + 51 We consider the new divisor 102 and new remainder 51, and apply the division lemma to obtain 102 = 51 x 2 + 0 Since the remainder is zero, the process stops.