Firstly, the HCF of 657 and 963 is to be found.
By applying Euclid’s division lemma, we get
963 = 657 x 1 + 306.
Here, the remainder ≠ 0 and so we apply Euclid’s division lemma on divisor 657 and remainder 306
657 = 306 x 2 + 45.
Now, continue applying division lemma till the remainder becomes 0.
306 = 45 x 6 + 36.
Again, the remainder ≠ 0
45 = 36 x 1 + 9.
Again, the remainder ≠ 0
36 = 9 x 4 + 0.
Now, the remainder = 0.
Hence, the last divisor is the H.C.F of 657 and 963 i.e., 9
So, this HCF is expressed as a linear combination which given as,
9 = 657 x + 936 (-15).
Solving for x, we get
9 = 657 x - 14445
9 + 14445 = 657 x
14454 = 657 x
⇒ x = 14454 / 657
∴ x = 22.
