If the HCF of 657 and 963 is Expressible in the Form 657x + 963x − 15, Find x

Video Explanation

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Solution

Question: If the HCF of 657 and 963 is expressible in the form 657x + 963x − 15, find the value of x.

Step 1: Find the HCF of 657 and 963

Using Euclid’s division algorithm:

963 = 657 × 1 + 306

657 = 306 × 2 + 45

306 = 45 × 6 + 36

45 = 36 × 1 + 9

36 = 9 × 4 + 0

Since the remainder is zero,

∴ HCF (657, 963) = 9

Step 2: Use the Given Expression

Given:

HCF = 657x + 963x − 15

HCF = (657 + 963)x − 15

HCF = 1620x − 15

Substitute HCF = 9

9 = 1620x − 15

1620x = 24

x = 24 / 1620

x = 2 / 135

Final Answer

∴ The value of x = 2 / 135.

Conclusion

Thus, by finding the HCF using Euclid’s division algorithm and comparing it with the given expression, we get the value of x = 2 / 135.