Question

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

Answer 1

SOLUTION :  

First ,we need to find the H.C.F of 657 and 963

Here 963 > 657

Let a = 963 and b = 657

963 = 657 x 1+ 306.

[By applying division lemma, a = bq + r]

Here, remainder = 306 ≠ 0, so take new dividend as 657 and new divisor as 306

Let a = 657 and b= 306

657 = 306 x 2 + 45.

[By applying division lemma, a = bq + r]

Here, remainder = 45 ≠ 0, so take new dividend as 306 and new divisor as 45.

Let a = 306 and b= 45

306 = 45 x 6 + 36.

[By applying division lemma, a = bq + r]

Here, remainder = 36 ≠ 0, so take new dividend as 45 and new divisor as 36..

Let a = 45 and b= 36

45 = 36 x 1 + 9.

[By applying division lemma, a = bq + r]

Here, remainder = 9 ≠ 0, so take new dividend as 36 and new divisor as 9.

Let a = 36 and b= 9

36 = 9 x 4 + 0.

Here, remainder is zero and divisor is 9

Hence ,H.C.F. of 657 and 963 is 9.

 H.C.F. = 9.

H.C.F = 657x + 936 (-15)

[Given]

9 = 657x - 14445

9 + 14445 = 657x

14454 = 657x

x =14454/657

x = 22.

Hence , the value of x is 22.

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Answer 2

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A DETAILED ANSWER ONLY FOR YOU :-


First, we have to find HCF of 657 and 963

Now, 657 = 9*63

         963 = 9*107

So, HCF(657, 963) = 9

Since HCF is expressed in the form of 657x +  963 * (-15)

So, 657x +  963 * (-15) = 9

=> 657x - 963 * 15 = 9

=> 657x - 14445 = 9

=> 657x = 14445 + 9

=> 657x = 14454

=> x = 14454/657

=> x = 22

So, the value of x is 22

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