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. EXERCISE 1.11. Use Euclid's division algorithm to find the HCF of:() 135 and 225(ii) 196 and 38220(ii) 867 a2. Show that any positive odd integer is of the form 6q+1, or 6q+3, or 6 |
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Answer» take 135 outside as the no to be divided (I) 135,225 Since 225 > 135, we apply the division lemma to 225 and 135 to obtain 225 = 135 × 1 + 90 Since remainder 90 ≠ 0 , we apply the division lemma to 135 and 90 to obtain 135 = 90 × 1 + 45 We consider the new divisor 90 and new remainder 45, and apply the division lemma to obtain 90 = 2 × 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 × 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. use Euclid's division algorithm to find the HCF of 135and 225 |
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