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Find out H.C.F. by Vedic method. (i) 8, 12 (ii) 38, 57 (iii) 117, 195 (iv) 99,165, 231 |
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Answer» Finding H.C.F. by vedic method, (i) 8, 12 First difference = 12 – 8 = 4 Thus, possible H.C.F. = 4 Second difference =8 – 4 = 4 ∵ First difference = Second difference ∴ H.C.F. of 8 and 12 = 4 (ii) 38, 57 First difference = 57 – 38 = 19 Thus, possible H.C.F. = 19 Second difference = 38 – 19 = 19 ∵ First difference = Second difference ∴ H.C.F of 38 and 57 = 19 (iii) 117,195 First difference = 195 – 117 = 78 Thus, possible H.C.F = 78 Second difference = 117 – 78 = 39 Thus, possible H.C.F = 39 Third difference = 78 – 39 = 39 ∵ Second difference = Third difference ∴ HCF 117 and 195 = 39 (iv) 99, 165, 231 Addition of two numbers = 99 + 231 = 330 First difference = 99 + 231 – 165 = 165 Thus, possible H.C.F = 165 Second difference = 231 – 165 = 66 Thus, possible H.C.F = 66 Third difference = 99 – 66 = 33 Thus, possible H.C.F = 33 ∵ Possible H.C.F is a factor of 66. ∴ HCF of 99, 165 and 231 = 33 |
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