Question

If the HCF of 657 and 963 is expressible in the form
657n + 963x (-15), find n.​

Answer 1

HCF of 657 and 963

By Using Euclid's division lemma to 657 and 963 we get.

• 963= 657×1+306

Since Remainder ≠0 we apply division lemma to Divisor 657 and remainder 306 to get,

• 657=306×2+45

Since Remainder ≠0 we apply division lemma to Divisor 306 and remainder 45 to get,

• 306=45×6+36

Since Remainder ≠0 we apply division lemma to Divisor 45 and remainder 36 to get,

• 45=36×1+9

Since Remainder ≠0 we apply division lemma to Divisor 36 and remainder 9 to get,

• 36=9×4+0

Since Remainder = 0

HCF of 657 and 963 = 9

→9= 657×n+963×(-15)

→9= 657×n-14445

→657n=9+14445

→657n=14454

→n=14454/657

• n=22