Use Euclids division algorithm to find the HCF of 210 and 55

1.	Use Euclids division algorithm to find the HCF of 210 and 55
Answer» Using Euclid's division algorithm. 210 = (553) + 45 55 = (451) + 10 45 = (104) + 5 10 = (52) + 0 So, the remainder is 0 at the last stage, so HCF of 210 and 55 is 5. ∴ 5 = (210*5) + 55y ⇒ 5 = 1050 + 55y ⇒ - 55y = 1050 - 5 ⇒ - 55y = 1045 ⇒ y = - 1045/55 ⇒ y = - 19 Hence, the value of x is 5 and y is - 19

Answer»

Using Euclid's division algorithm.

210 = (55*3) + 45

55 = (45*1) + 10

45 = (10*4) + 5

10 = (5*2) + 0

So, the remainder is 0 at the last stage, so HCF of 210 and 55 is 5.

∴ 5 = (210*5) + 55y

⇒ 5 = 1050 + 55y

⇒ - 55y = 1050 - 5

⇒ - 55y = 1045

⇒ y = - 1045/55

⇒ y = - 19

Hence, the value of x is 5 and y is - 19

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