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Question

If the HCF of 657 and 963 is expressible in the form 657 x+963×15, find x.

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Solution

By Euclid's division algorithm
963=657×1+306
657=306×2+45
306=45×6+36
45=36×1+9
36=9×4+0

Since the reminder becomes here so HCF of 657 and 963 is 9 Now

657x+963×(15)=HCF of these number
657x+963x(15)=9
657x=14454
x=22

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