If the HCF of 657 and 963 is expressible in the form 657x + 963x − 1

1.	If the HCF of 657 and 963 is expressible in the form 657x + 963x − 15, find x.
Answer» 657 and 963 By applying Euclid’s division lemma 963 = 657 × 1 + 306 Since remainder ≠ 0, apply division lemma on division 657 and remainder 306 657 = 306 × 2 + 45 Since remainder ≠ 0, apply division lemma on division 306 and remainder 45 306 = 45 × 6 + 36 Since remainder ≠ 0, apply division lemma on division 45 and remainder 36 45 = 36 × 1 + 19 Since remainder ≠ 0, apply division lemma on division 36 and remainder 19 36 = 19 × 4 + 0 ∴ HCF = 657 Given HCF = 657 + 963 × (-15) ⇒ 9 = 657 × −1445 ⇒ 9 + 14445 = 657 x ⇒ 657x = 1445y ⇒ x = 1445y/657 ⇒ x = 22

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

Answer»

657 and 963
By applying Euclid’s division lemma
963 = 657 × 1 + 306
Since remainder ≠ 0, apply division lemma on division 657 and remainder 306
657 = 306 × 2 + 45
Since remainder ≠ 0, apply division lemma on division 306 and remainder 45
306 = 45 × 6 + 36
Since remainder ≠ 0, apply division lemma on division 45 and remainder 36
45 = 36 × 1 + 19
Since remainder ≠ 0, apply division lemma on division 36 and remainder 19
36 = 19 × 4 + 0
∴ HCF = 657
Given HCF = 657 + 963 × (-15)
⇒ 9 = 657 × −1445
⇒ 9 + 14445 = 657 x
⇒ 657x = 1445y
⇒ x = 1445y/657

⇒ x = 22

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