Exercise 1.1, 2.1 solution NCERT Mathematics
NCERT SOLUTION CLASS XTH: REAL NUMBERS Q1: Use Euclid’s division algorithm to find the HCF of (I) 135 and 225 (ii) 196 and 38220 (iii) 867, 255 Solution To start the solution, first, we write the Euclid division lemma Let a, b, q, and r be integers such that a = bq + r. Where 0 < a, a is the dividend, b is the quotient, and r is the remainder. if the remainder r = 0, then HCF = b. For the HCF of 135 and 225 225 = 135x1 + 90 135 = 90x1 + 45 90 = 45x2 + 0. Here, the remainder is 0; hence, we can consider 45 as an HCF HCF = 45 (ii) 38220 is greater than 196, so divide 38220 by 196 and note down the quotient and remainder: a = 38220, b = 196, r = 0 We can write using the Euclidean division lemma 38220 = 196x195 + 0 Hence HCF = 196 (iii) 867 and 255 In this question, 867 is greater than 255, so we divide 855 by 255 and note the remainder and t...