Question

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

Answer 1

Answer:

Using Euclid’s Division  Lemma

a= bq+r / Dividend= Divisor * Quotient + Remainder

=963=657×1+306  

=657=306×2+45  

=306=45×6+36  

=45=36×1+9  

=36=9×4+0  

∴HCF is 9

9=657x - (963*15)   657x= 14454  

X=22

           (Ans)

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Answer 2

Given: Two numbers-  657 and 963

           HCF of 657 and 963 is expressible in the form $657x + 963 (-15)$

To find: The value of $x$

Solution:

Using Euclid's Division Lemma (a = bq + r), we need to find the HCF of 657 and 963.

Here a = 963 and b = 657

We get,

⇒ 963 = 657 × 1 + 306

Now, we need to apply Euclid's Division Lemma again taking a = 657 and b = 306

⇒ 657 = 306 × 2 + 45

Taking a = 306 and b = 45

⇒ 306 = 45 × 6 + 36

Taking a = 45 and b = 36

⇒ 45 = 36 × 1 + 9

Taking a = 36 and b = 9

⇒ 36 = 9 × 4 + 0

As the remainder has become 0, we can't proceed further.

The divisor is 9 when remainder is 0.

So, HCF of 657 and 963 is 9.

Now, according to the question,

⇒ 9 = $657x + 963 (-15)$

⇒ $657x = 9 + 14445 = 14454$

⇒ $x = \frac{14454}{657} = 22$

Hence, the value of $x$ is 22.