Question

Express the HCF of 210 and 66 in the form of 210x + 66y

Answer 1

Answer:

6 = 16 × (66) - 5 × (210)

Step-by-step explanation:

We know that by division algorithm we can write 210 as

210 = 66 × 3 + 12      .......(1)

And by again division algorithm on 66 we get

66 = 12 × 5 + 6          .......(2)

And again applying division algorithm on 12 we get

12 = 6 × 2                  .........(3)

This implies H.C.F of 210 and 66 = 6

And

By equation (2) we get

6 = 66 - 12 × 5

And using equation (1) we get

6 = 66 - (210 - 66 × 3) × 5

  = 66 - 210 × 5 + 15 × (66)

  = 16 × (66) - 5 × (210)  

So

6 = 16 × (66) - 5 × (210)

where 6 is H.C.F of 210 and 66

So we write the H.C.F of 210 and 66 as 210x + 66y where x = -5 and y = 16

Answer 2

Answer:

35x+11y=1

Step-by-step explanation:

The hcf of 210,66

210=3*2*35

66=3*2*11

So hcf=6

So 210x+66y=6->35x+11y=1