Question

for some a and b , if hcf of 55 and 210 is 210a+55b then find the value of a and b

Answer 1

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Answer 2

Answer:

a = 5 and b = -19

Step-by-step explanation:

HCF(55,210) = 210a + 55b

210 = 55×3 + 45

55 = 45×1 + 10

45 = 10×4 + 5

10 = 5×2 + 0

Hence, HCF(55,210) = 5

Now, 5 = 45 - 10×4

5 = 45 - (55 - 45×1)×4

5 = 45×5 - 55×4

5 = (210 - 55×3)×5 - 55×4

5 = 210×5 - 55×19

5 = 210×5 + 55×(-19)

Now, comparing it with given expression

⇒ a = 5 and b = -19