Question

If the HCF of 63 and 162 is expressible in the form 65 m + 117n , then
find the
value of m and n .

Answer 1

Answer:

m= 2

n= -1

Step-by-step explanation:

Hello there !

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

Hope this Helped You !

Answer 2

Answer:

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