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Find the hcf of 65 and …

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Find the hcf of 65 and 117 express in the form of 65m+117n
  • 1 answers

Shivam The Galaxy 6 years, 11 months ago

Euclid's Division Lemma :- a = bq +r 117 > 65 117 = 65 × 1 + 52 ----> [ 2 ] 65 = 52 x 1 + 13 -----> [1] 52 = 13 x 4 + 0 HCF = 13 13 = 65m + 117n From [ 1] , 13 = 65 - 52 x 1 From [2] , 52 = 117 - 65 x 1 ----> [3] Hence , 13 = 65 - [ 117 - 65 x 1 ] ------> from [3] = 65 x 2 - 117 = 65 x 2 + 117 x [-1 ] m = 2 n = -1
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