Question

20. Find the hcf of 55 and 210. Express it as a linear combination of 55 and 210, i.E. Hcf of 55 and 210=210a+ 55b, for some a and b.

Answer 1

$\mathfrak{\huge{Hi !}}$

210 = 55 × 3 + 45

55 = 45 × 1 + 10

45 = 10 × 4 + 5

10 = 5 × 2 + 0

$\underline{\sf{HCF = 5}}$

5 = 45 - 10(4)

5 = 45 - (55 - 45)(4)

5 = 45 - 55(4) + 45(4)

5 = (210 - 55(3)) - 55(4) + (210 - 55(3))(4)

5 = 210 - 55(3) - 55(4) + 210(4) - 55(12)

$\boxed{\bf{a = 5, b = (-19)}}$