Question

If the HCF of 65 and 117 can be written as 65m+117n. Find the value of m and n
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Answer 1

Step-by-step explanation:

117 > 65  [ a = bq + r]

117 = a

65 = b

                                         

117 = 65 * 1 + 52 ----> (1)

65 = 52 * 1 + 13 ------>(2)

52 = 13 * 4 + 0  

HCF  = 13

13 = 65m + 117n

From (2) ---> 65 = 52 + 13 ==>  13 = 65 - 52 ----> (3)

From (1) ----> 117 = 65 + 52 ==> 52 = 117 - 65 ---> (4)

Sub (4) in (3)

13 = 65 - ( 117 - 65 )

13 = 65 * 2 - 117

m = 2

n = -1