Maths chapter 1 exercise 1.1 question …

(i) HCF of 135 and 225: Applying the Euclid’s lemma to 225 and 135, (where 225 > 135), we get 225 = (135 × 1) + 90 Since, 90 ≠ 0, therefore, applying the Euclid’s lemma to 135 and 90, we have: 135 = (90 × 1) + 45 But 45 ≠ 0 ∴ Applying Euclid’s Lemma to 90 and 45, we get 90 = (45 × 2) + 0 Here, r = 0, so our process stops. Since, the divisor at the last step is 45, ∴ HCF of 225 and 135 is 45. (ii) HCF of 196 and 38220: We start dividing the larger number 38220 by 196, we get 38220 = (196 × 195) + 0 ∵ r = 0 ∴ HCF of 38220 and 196 is 196. (iii) HCF of 867 and 255: Here, 867 > 255 ∴ Applying Euclid’s Lemma to 867 and 255, we get 867 = (255 × 3) + 102 Since, 102 ≠ 0, therefore, applying the Euclid’s lemma to 255 and 102, we have: 255 = (102 × 2) + 51 But 51 ≠ 0 ∴ Applying Euclid’s Lemma to 102 and 51, we get 102 = (51 × 2) + 0 Here, r = 0, so our process stops. Since, the divisor at the last step is 51, ∴ HCF of 867 and 255 is 51.

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