Question

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

Answer 1

HCF of 657 and 963 = 3*3 = 9
657x + 963*(-15)
657*x - 14445 = 9
657*x = 9+14445
657*x = 14454
x = 14454/657
x = 22

Answer 2

Solution:-

Applying Euclid’s Division Algorithm,

a = bq + r

where, 0 < r < b

Applying Euclid’s Division Lemma to 963 > 657.

963 = 657 × 1 + 306

Applying Euclid’s Division Lemma to 657 > 306.

657 = 306 × 2 + 45

Applying Euclid’s Division Lemma to 306 > 45.

306 = 45 × 6+ 36

Applying Euclid’s Division Lemma to 45 > 36.

45 = 36 × 1+ 9

Applying Euclid’s Division Lemma to 36 > 9.

36 = 9 × 4 + 0

[∴HCF is 9]

Now,

9 = 657x - (963 × 15)

657x = 14454

[∴x=22]