If the HCF of 657 and963 …

Given numbers are 657 and 963 .

Here, 657 < 963 

By using Euclid's Division algorithmm , we get
963 = (657  × 1) + 306

Here , remainder = 306 .

So, On taking 657 as new dividend and 306 as the new divisor and then apply Euclid's Division lemma, we get
657 = (306  × 2) + 45

Here, remainder = 45 

So, On taking 306 as new dividend and 45 as the new divisor and then apply Euclid's Division lemma, we get
306 = (45  × 6) + 36

Here, remainder = 36

So, On taking 45 as new dividend and 36 as the new divisor and then apply Euclid's Division lemma, we get
45 = (36  × 1) + 9
Here, remainder = 9

So, On taking 36 as new dividend and 9 as the new divisor and then apply Euclid's Division lemma, we get

36 = (9  × 4) + 0
Here , remainder = 0 and last divisor is 9. 

Hence, HCF of  657 and 963 = 9.

∴ 9 = 657x + 963(-15)
⇒ 9 = 657x - 14445
⇒ 657x = 9 + 14445
⇒ 657x = 14454
⇒x = 14454/657
⇒ x =22