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

Question

If the HCF of 657 and 963 is expressible in the form 657 x + 963 &#xD7; -15, find x.

Philoid · Accepted Answer

Prime factors of 657: 3 × 3 × 73

Prime factors of 963: 3 × 3 × 107

HCF of 657 and 963 = 3 × 3 = 9

According to question:

9 = 657x + 963 × -15

9 = 657x - 14445

9 + 14445 = 657x

∴ x = 14454/657 = 22

Therefore x = 22