Question

Use euclid division algorithm to find the hcf of 210 and 55 if hcf is expressible in the form of 210x+55y find x and y

Answer 1

the HCF of 210 and 55

210=55*3+45

55=45*1+10

45=10*4+5

10=5*2+0

therefore 5 is the hcf

5=210x+55y

Answer 2

Solution :-

HCF of 210 and 55

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

Answer.