Question

5) If the HCF of 55 and 99 is expressible in the form 55x + 99y, find x and y 6) find HCF of 65 and 117 and express it in the form 65x + 117y.Also find x and y

Answer 1

Given :  55 & 99  ,   65 & 117

To find : HCF & express HCF in form 55x + 99y  & 65x + 117y  

Solution:

HCF of 55 & 99

99 = 55 *1  + 44

55 = 44*1  + 11

44 = 11 * 4  

11 Is the HCF

55 = 44*1  + 11

=> 11 = 55 - 44*1

=> 11 =  55 - ( 99 - 55*1) * 1

=> 11 = 55 *2 + 99*(-1)

11 = 55x + 99y

x = 2  ,  y  =  -1  

117 = 65 * 1  + 52

65 = 52 * 1  + 13

52 = 13 * 4

=> 13 is HCF

13  = 65  - 52* 1

=> 13 = 65  -  (117 - 65 * 1)

=> 13 = 65 *2  + 117(-1)

13 = 65x + 117y

=> x = 2 , y = -1

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