Use Euclids division algorithm to find the HCF of i 135 and 225 ii 196 and 38220 iii 867 and 255 iv ...

Question

Use Euclids division algorithm to find the HCF of i 135 and 225 ii 196 and 38220 iii 867 and 255 iv 184 230 and 276 v 136 170 and 255

Accepted Answer

Given integers here are 225 and 135 On comparing we find 225 135 So by applying Euclids division lemma to 225 and 135 we get 867 225 x 3 192 Since the remainder 0 So we apply the division lemma to the divisor 135 and remainder 90 135 90 x 1 45 Now we apply the division lemma to the new divisor 90 and remainder 45 90 45 x 2 0 Since the remainder at this stage is 0 the divisor will be the HCF Hence the HCF of 225 and 135 is 45 ii 196 and 38220 Given integers here are 196 and 38220 On comparing we find 38220 196 So by applying Euclids division lemma to 38220 and 196 We get 38220 196 x 195 0 Since the remainder at this stage is 0 the divisor will be the HCF Hence the HCF of 38220 and 196 is 196 iii 867 and 255 Given integers here are 867 and 255 On comparing we find 867 255 So by applying Euclids division lemma to 867 and 225 we get 867 225 x 3 192 Since the remainder 192 0 So we apply the division lemma to the divisor 225 and remainder 192 We get 225 192 x 1 33 Now we apply the division lemma to the new divisor 192 and remainder 33 We get 192 33 x 5 27 Now we apply the division lemma to the new divisor 33 and remainder 27 We get 33 27 x 1 6 Now we apply the division lemma to the new divisor 27 and remainder 6 We get 27 6 x 4 3 Now we apply the division lemma to the new divisor 27 and remainder 6 We get 6 3 x 2 0 Since the remainder at this stage is 0 the divisor will be the HCF Hence the HCF of 867 and 255 is 3 iv 184 230 and 276 Lets first choose 184 and 230 to find the HCF by using Euclids division lemma Thus we obtain 230 184 x 1 46 Since the remainder 46 0 So we apply the division lemma to the divisor 184 and remainder 46 We get 184 46 x 4 0 The remainder at this stage is 0 the divisor will be the HCF ie 46 for 184 and 230 Now we again use Euclids division lemma to find the HCF of 46 and 276 And we get 276 46 x 6 0 So this stage has remainder 0 Thus the HCF of the third number 276 and 46 is 46 Hence the HCF of 184 230 and 276 is 46 v 136 170 and 255 Lets first choose 136 and 170 to find the HCF by using Euclids division lemma Thus we obtain 170 136 x 1 34 Since the remainder 34 0 So we apply the division lemma to the divisor 136 and remainder 34 We get 136 34 x 4 0 The remainder at this stage is 0 the divisor will be the HCF ie 34 for 136 and 170 Now we again use Euclids division lemma to find the HCF of 34 and 255 And we get 255 34 x 7 17 Since the remainder 17 0 So we apply the division lemma to the divisor 34 and remainder 17 We get 34 17 x 2 0 So this stage has remainder 0 Thus the HCF of the third number 255 and 34 is 17 Hence the HCF of 136 170 and 255 is 17

RD Sharma Solutions Class 10 Mathematics Solutions for Real Numbers Exercise 1.2 in Chapter 1 - Real Numbers