2. Find the HCF of 65 and 117 and expressit as a linear combination of

1.	2. Find the HCF of 65 and 117 and expressit as a linear combination of 65 and 117.
Answer» 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] , 13 = 65 - [ 117 - 65 x 1 ] ------> from [3] = 65 x 2 - 117 = 65 x 2 + 117 x [-1 ] m = 2n = -1

2. Find the HCF of 65 and 117 and expressit as a linear combination of 65 and 117.

Answer»

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] ,

13 = 65 - [ 117 - 65 x 1 ] ------> from [3]

= 65 x 2 - 117

= 65 x 2 + 117 x [-1 ]

m = 2n = -1