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HCF (38220, 196) :

38220 = 196 * 195 + 0 => HCF is 196.

38220 = 196 * 194 + 196

=> 196 = 38220 * 1 - 196 * 194

Also, 196 = 196 * 1 + 38220 * 0

Also, 38220 = 196 * 196 - 196

=> 196 = 196 * 196 - 38220 * 1

= 196 * x + 38220 * y

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The normal way of finding the HCF and expressing the HCF as a linear combination of the given numbers is as follows:

HCF (32 , 20) :

32 = 20 * 1 + 12

20 = 12 * 1 + 8

12 = 8 * 1 + 4

8 = 4 * 2 + 0 => 4 is the HCF.

4 = 12 - 8 * 1

= 12 - (20 - 12 * 1 )

= 2 * 12 - 20

= 2 * (32 - 20 * 1 ) - 20

38220 = 196 * 195 + 0 => HCF is 196.

38220 = 196 * 194 + 196

=> 196 = 38220 * 1 - 196 * 194

*=> 196 = 38220 * y + 196 * x, where y = 1 and x = - 194*Also, 196 = 196 * 1 + 38220 * 0

*So, x = 1 and y = 0.*Also, 38220 = 196 * 196 - 196

=> 196 = 196 * 196 - 38220 * 1

= 196 * x + 38220 * y

*So x = 196 and y = -1*===============

The normal way of finding the HCF and expressing the HCF as a linear combination of the given numbers is as follows:

*This is an example to demonstrate the technique.*HCF (32 , 20) :

32 = 20 * 1 + 12

20 = 12 * 1 + 8

12 = 8 * 1 + 4

8 = 4 * 2 + 0 => 4 is the HCF.

4 = 12 - 8 * 1

= 12 - (20 - 12 * 1 )

= 2 * 12 - 20

= 2 * (32 - 20 * 1 ) - 20

*4 = 2 * 32 - 3 * 20*