Question

find the hcf of 200 and 275 and express it in the form of 275x + 200y

Answer 1

This is the answer to your question

Answer 2

_______________

For HCF(200,275),By Euclid's Division Lemma,

=> 275 = 200 x 1 + 75 ---------(2)

=> 200 = 75 x 2 + 50 --------(1)

=> 75 = 50 x 1 + 25 <<<<<<<< answer

=> 50 = 25 x 2 + 0

Thus HCF = 25

Expression part

We have

=> 75 = 50 x 1 + 25

=> 25 = 75 - (50 x 1)

Now replace 50 from (1)

=> 25 = 75 - [200 - (75 x 2)]

=> 25 = 75 - 200 + (75 x 2)

=> 25 = 75(3) - 200(1)

Now replace 75 from (2)

=> 25 = [275 - (200 x 1)]3 - 200(1)

=> 25 = 275(3) - 200(2)

=> 25 = 275x + 200y <<<< Answer

where x = 3 and y = - 2